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6	<title>YALMIP - Command reference</title>
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14	<body>
15
16	<div align="left">
17	<table border="0" cellpadding="4" cellspacing="3" style="border-collapse: collapse" width="100%" align="left">
18	<tr>
19	<td width="100%" align="left" height="100%" valign="top">
20	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table30">
21	<tr>
22	<td class="tableheader">
23	<p class="tableheader"><a name="assign">ASSIGN</font></a></p>
24	</td>
25	</tr>
26	<tr>
27	<td>
28	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table31">
29	<tr>
30	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
31	Syntax</th>
32	<td class="code" valign="top" nowrap width="100%"><code>assign(X,Y)</code></td>
33	</tr>
34	<tr>
35	<td class="tabxpl">
36	<table border="0" id="table32">
37	<tr>
38	<td>
39	<p align="right"><font face="Courier New" size="2">X:</font></p>
40	</td>
41	<td>sdpvar object</td>
42	</tr>
43	<tr>
44	<td>
45	<p align="right"><font face="Courier New" size="2">Y:</font></p>
46	</td>
47	<td>double</td>
48	</tr>
49	</table>
50	</td>
51	</tr>
52	<tr>
53	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
54	Description</th>
55	</tr>
56	<tr>
57	<td class="tabxpl">assign is used to explicitly assigning the value obtained
58	when applying the command double on an
59	<a href="reference.htm#sdpvar">sdpvar</a> object</td>
60	</tr>
61	<tr>
62	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
63	Examples</th>
64	</tr>
65	<tr>
66	<td class="tabxpl">Variables are initialized as NaNs<table cellpadding="10" width="100%" id="table33">
67	<tr>
68	<td class="xmpcode">
69	<pre>x = sdpvar(1,1);
70	double(x)
71	<font color="#000000">ans =
72	NaN</font></pre>
73	</td>
74	</tr>
75	</table>
76	<p>By using <a href="reference.htm#assign">assign</a>, this
77	value can be altered </p>
78	<table cellpadding="10" width="100%" id="table34">
79	<tr>
80	<td class="xmpcode">
81	<pre>assign(x,1)
82	double(x)
83	<font color="#000000"> ans =
84	1</font></pre>
85	</td>
86	</tr>
87	</table>
88	<p>By default, inconsistent assignments generate an error message.</p>
89	<table cellpadding="10" width="100%" id="table35">
90	<tr>
91	<td class="xmpcode">
92	<pre>t = sdpvar(1,1);x = [t t];
93	assign(x,[1 2])
94	<font color="#000000">??? Error using ==> sdpvar/assign
95	Inconsistent assignment</font></pre>
96	</td>
97	</tr>
98	</table>
99	<p>With a third argument, a least squares assignment is obtained</p>
100	<table cellpadding="10" width="100%" id="table36">
101	<tr>
102	<td class="xmpcode">
103	<pre>t = sdpvar(1,1);x = [t t];
104	assign(x,[1 2],1)
105	double(x)
106
107	<font color="#000000">ans =
108
109	1.5000 1.5000</font></pre>
110	</td>
111	</tr>
112	</table>
113	</td>
114	</tr>
115	<tr>
116	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
117	Related commands</th>
118	</tr>
119	<tr>
120	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a></td>
121	</tr>
122	</table>
123	</td>
124	</tr>
125	</table>
126	<p> </p>
127	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
128	<tr>
129	<td class="tableheader">
130	<p class="tableheader"><a name="binary">BINARY</a></p>
131	</td>
132	</tr>
133	<tr>
134	<td>
135	<table cellspacing="0" cellpadding="4" width="100%" border="0">
136	<tr>
137	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
138	Syntax</th>
139	<td class="code" valign="top" nowrap width="100%"><code>c = binary(x)</code></td>
140	</tr>
141	<tr>
142	<td class="tabxpl">
143	<table border="0">
144	<tr>
145	<td>
146	<p align="right"><font face="Courier New">c:</font></p>
147	</td>
148	<td>sdpvar object (only useful in <a href="reference.htm#lmi">
149	set</a>)</td>
150	</tr>
151	<tr>
152	<td>
153	<p align="right"><font face="Courier New">x:</font></p>
154	</td>
155	<td>sdpvar object</td>
156	</tr>
157	</table>
158	</td>
159	</tr>
160	<tr>
161	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
162	Description</th>
163	</tr>
164	<tr>
165	<td class="tabxpl">binary is used to constrain a variables to be binary.</td>
166	</tr>
167	<tr>
168	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
169	Examples</th>
170	</tr>
171	<tr>
172	<td class="tabxpl">
173
174	<p>Setting up a binary linear program <b>{min c<sup>T</sup>x
175	subject to Ax≤b}</b> can be done as</p>
176
177	<table cellpadding="10" width="100%">
178	<tr>
179	<td class="xmpcode">
180	<pre>x = binvar(n,1);
181	solvesdp(set(Ax<b),c'x)</pre>
182	</td>
183	</tr>
184	</table>
185	<p>or</p>
186	<table cellpadding="10" width="100%">
187	<tr>
188	<td class="xmpcode">
189	<pre>x = sdpvar(n,1);
190	solvesdp(set(Ax<b)+set(binary(x)),c'x)</pre>
191	</td>
192	</tr>
193	</table>
194	<p>Note, the binary constraint is imposed on the involved variables,
195	not the actual <a href="reference.htm#sdpvar">sdpvar</a> object. Hence,
196	the following two constraints are equivalent </p>
197	<table cellpadding="10" width="100%">
198	<tr>
199	<td class="xmpcode">
200	<pre>F = set(binary(x));
201	F = set(binary(pi+sqrt(2)*x));</pre>
202	</td>
203	</tr>
204	</table>
205	</td>
206	</tr>
207	<tr>
208	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
209	Related commands</th>
210	</tr>
211	<tr>
212	<td class="tabxpl"><a href="reference.htm#intvar">intvar</a>,
213	<a href="reference.htm#sdpvar">sdpvar</a>,
214	<a href="reference.htm#binvar">binvar</a>, <a href="#set">set</a></td>
215	</tr>
216	</table>
217	</td>
218	</tr>
219	</table>
220	<p> </p>
221	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
222	<tr>
223	<td class="tableheader">
224	<p class="tableheader"><a name="binvar">BINVAR</a></p>
225	</td>
226	</tr>
227	<tr>
228	<td>
229	<table cellspacing="0" cellpadding="4" width="100%" border="0">
230	<tr>
231	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
232	Syntax<p> </p>
233	</th>
234	<td class="code" valign="top" nowrap width="100%"><code>x = binvar(n,m,'field','type')</code></td>
235	</tr>
236	<tr>
237	<td class="tabxpl">
238	<table border="0">
239	<tr>
240	<td>
241	<p align="right"><font face="Courier New" size="2">n:</font></p>
242	</td>
243	<td>Height</td>
244	</tr>
245	<tr>
246	<td>
247	<p align="right"><font face="Courier New" size="2">m:</font></p>
248	</td>
249	<td>Width</td>
250	</tr>
251	<tr>
252	<td>
253	<p align="right"><font face="Courier New" size="2">'field':</font></p>
254	</td>
255	<td>char {'real','complex'}</td>
256	</tr>
257	<tr>
258	<td>
259	<p align="right"><font face="Courier New" size="2">'type':</font></p>
260	</td>
261	<td>char {'symmetric','full','hermitian','toeplitz','hankel','skew'}</td>
262	</tr>
263	</table>
264	</td>
265	</tr>
266	<tr>
267	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
268	Description</th>
269	</tr>
270	<tr>
271	<td class="tabxpl">binvar is used to define symbolic decision variables
272	with binary elements.</td>
273	</tr>
274	<tr>
275	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
276	Examples</th>
277	</tr>
278	<tr>
279	<td class="tabxpl"><p>A scalar binary variable is defined with</p><table cellpadding="10" width="100%">
280	<tr>
281	<td class="xmpcode">
282	<pre>P = binvar(1,1)</pre>
283	</td>
284	</tr>
285	</table>
286	<p>For more examples, see <a href="reference.htm#sdpvar">sdpvar</a>.</p>
287	</td>
288	</tr>
289	<tr>
290	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
291	Related commands</th>
292	</tr>
293	<tr>
294	<td class="tabxpl"><a href="reference.htm#intvar">intvar</a>,
295	<a href="reference.htm#sdpvar">sdpvar</a>,
296	<a href="reference.htm#integer">integer</a>,
297	<a href="reference.htm#binary">binary</a>, <a href="#set">set</a></td>
298	</tr>
299	</table>
300	</td>
301	</tr>
302	</table>
303	<p> </p>
304	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table53">
305	<tr>
306	<td class="tableheader">
307	<p class="tableheader"><a name="blkvar">BLKVAR</a></p>
308	</td>
309	</tr>
310	<tr>
311	<td>
312	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table54">
313	<tr>
314	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
315	Syntax<p> </p>
316	</th>
317	<td class="code" valign="top" nowrap width="100%"><code>X = blkvar</code></td>
318	</tr>
319	<tr>
320	<td class="tabxpl">
321	<table border="0" id="table55">
322	<tr>
323	<td>
324	<p align="right"><font face="Courier New" size="2">X:</font></p>
325	</td>
326	<td>Container for block matrix</td>
327	</tr>
328	</table>
329	</td>
330	</tr>
331	<tr>
332	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
333	Description</th>
334	</tr>
335	<tr>
336	<td class="tabxpl">blkvar is used to handle block matrices in a
337	more symbolic fashion.</td>
338	</tr>
339	<tr>
340	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
341	Examples</th>
342	</tr>
343	<tr>
344	<td class="tabxpl">Consider the 3x3 block matrix <code>[A B 0;B' C
345	D;0 D' E]</code>. Using standard YALMIP and MATLAB code, we would define this using
346	concatenations. <table cellpadding="10" width="100%" id="table56">
347	<tr>
348	<td class="xmpcode">
349	<pre>n = 5;
350	m = 3;
351	A = sdpvar(n,n);
352	B = randn(n,2);
353	E = sdpvar(m,m);
354	C = randn(2,2);
355	D = randn(2,m);</pre>
356	<pre>X = [A B zeros(n,m);B' C D;zeros(m,n) D' E];</pre>
357	</td>
358	</tr>
359	</table>
360	<p>By using a block variable, we can define blocks instead. </p>
361	<table cellpadding="10" width="100%" id="table57">
362	<tr>
363	<td class="xmpcode">
364	<pre>X = blkvar;
365	X(1,1) = A;
366	X(1,2) = B;
367	X(1,3) = 0;
368	X(2,2) = C;
369	X(2,3) = D;
370	X(3,3) = E;
371	X = sdpvar(X);</pre>
372	</td>
373	</tr>
374	</table>
375	<p>Dimension of 0 blocks do not have to be specified, they will be
376	automatically be derived, if possible, from the dimension of
377	other elements. Note that we only have to define one element of
378	symmetric pairs, YALMIP will automatically fill in the symmetric
379	counter-part. If no symmetric counter-part is found, the
380	corresponding block is filled with zeroes. Hence, the following
381	code is equivalent.</p>
382	<table cellpadding="10" width="100%" id="table58">
383	<tr>
384	<td class="xmpcode">
385	<pre>X = blkvar;
386	X(1,1) = A;
387	X(1,2) = B;
388	X(2,2) = C;
389	X(2,3) = D;
390	X(3,3) = E;
391	X = sdpvar(X);</pre>
392	</td>
393	</tr>
394	</table>
395	<p>Standard operators can typically be applied directly to the
396	block variable (but it is currently recommended to convert the
397	variable to an sdpvar object)</p>
398	<table cellpadding="10" width="100%" id="table59">
399	<tr>
400	<td class="xmpcode">
401	<pre>X = blkvar;
402	X(1,1) = A;
403	X(1,2) = B;
404	X(2,2) = C;
405	X(2,3) = D;
406	X(3,3) = E;
407	F = set(X > 0 ) + set(trace(X)==1);
408	% Recommended
409	X = sdpvar(X);
410	F = set(X > 0 ) + set(trace(X)==1);</pre>
411	</td>
412	</tr>
413	</table>
414	</td>
415	</tr>
416	<tr>
417	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
418	Related commands</th>
419	</tr>
420	<tr>
421	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a></td>
422	</tr>
423	</table>
424	</td>
425	</tr>
426	</table>
427	<p> </p>
428	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table44">
429	<tr>
430	<td class="tableheader">
431	<p class="tableheader"><a name="bounds">BOUNDS</font></a></p>
432	</td>
433	</tr>
434	<tr>
435	<td>
436	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table45">
437	<tr>
438	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
439	Syntax</th>
440	<td class="code" valign="top" nowrap width="100%"><code>bounds(X,lower,upper)</code></td>
441	</tr>
442	<tr>
443	<td class="tabxpl">
444	<table border="0" id="table51">
445	<tr>
446	<td>
447	<p align="right"><font face="Courier New" size="2">X:</font></p>
448	</td>
449	<td>sdpvar</td>
450	</tr>
451	<tr>
452	<td>
453	<p align="right"><font face="Courier New" size="2">lower:</font></p>
454	</td>
455	<td>double</td>
456	</tr>
457	<tr>
458	<td>
459	<p align="right"><font face="Courier New" size="2">upper:</font></p>
460	</td>
461	<td>double</td>
462	</tr>
463	</table>
464	</td>
465	</tr>
466	<tr>
467	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
468	Description</th>
469	</tr>
470	<tr>
471	<td class="tabxpl" height="26">bounds is used to add implicit
472	domain bounds on variables to improve big-M relaxations.</td>
473	</tr>
474	<tr>
475	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
476	Examples</th>
477	</tr>
478	<tr>
479	<td class="tabxpl">Variable bounds defined with the command bounds
480	are used to compute suitable constants when performing big-M
481	relaxations in
482	<a href="logic.htm">logic programming</a> and while creating MILP
483	models for <a href="extoperators.htm#milp">non-convex operators</a>. As an example, the following simple mixed
484	integer logic
485	program requires a big-M relaxation in YALMIP. To improve the
486	relaxation, we supply bounds on the variable <b>x</b>.<table cellpadding="10" width="100%" id="table47">
487	<tr>
488	<td class="xmpcode">
489	<pre>A1 = randn(10,3);
490	b1 = rand(10,1)*10;
491	A2 = randn(10,3);
492	b2 = rand(10,1)*10;
493	x = sdpvar(3,1);bounds(x,[-25;-25;-25],[25;25;25]);
494	F = set((A1x<=b1) \| (A1x <=b2));
495	solvesdp(F,sum(x))</pre>
496	</td>
497	</tr>
498	</table>
499	<p>Of course, standard MATLAB notation applies so if you have the
500	same bound on all variables, you only need to supply one scalar
501	bound.</p><table cellpadding="10" width="100%" id="table52">
502	<tr>
503	<td class="xmpcode">
504	<pre>A1 = randn(10,3);
505	b1 = rand(10,1)*10;
506	A2 = randn(10,3);
507	b2 = rand(10,1)*10;
508	x = sdpvar(3,1);bounds(x,-25,25);
509	F = set((A1x<=b1) \| (A1x <=b2));
510	solvesdp(F,sum(x))</pre>
511	</td>
512	</tr>
513	</table>
514	<p>Note that the big-M computation only take advantage of
515	bounds explicitly defined using the bounds command. Bounds defined using a
516	<a href="reference.htm#set">set</a> construction will not be detected or exploited. Hence, the
517	following problem will give rise to a MILP with weaker relaxations (big-M will be set to e 10<sup>4</sup>).</p>
518	<table cellpadding="10" width="100%" id="table49">
519	<tr>
520	<td class="xmpcode">
521	<pre>x = sdpvar(3,1);
522	F = set(-25 <= x<= 25) + set((A1x<=b1) \| (A1x <=b2));
523	solvesdp(F,sum(x))</pre>
524	</td>
525	</tr>
526	</table>
527	</td>
528	</tr>
529	<tr>
530	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
531	Related commands</th>
532	</tr>
533	<tr>
534	<td class="tabxpl"><a href="reference.htm#set">set</a></td>
535	</tr>
536	</table>
537	</td>
538	</tr>
539	</table>
540	<p> </p>
541	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
542	<tr>
543	<td class="tableheader">
544	<p class="tableheader"><a name="checkset">CHECKSET</a></p>
545	</td>
546	</tr>
547	<tr>
548	<td>
549	<table cellspacing="0" cellpadding="4" width="100%" border="0">
550	<tr>
551	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
552	Syntax</th>
553	<td class="code" valign="top" nowrap width="100%"><code>[p,d] = checkset(F)</code></td>
554	</tr>
555	<tr>
556	<td class="tabxpl">
557	<table border="0">
558	<tr>
559	<td>
560	<p align="right"><font face="Courier New" size="2">F:</font></p>
561	</td>
562	<td>set object</td>
563	</tr>
564	<tr>
565	<td>
566	<p align="right"><font face="Courier New">p</font><font face="Courier New" size="2">:</font></p>
567	</td>
568	<td>Primal constraint residuals</td>
569	</tr>
570	<tr>
571	<td>
572	<p align="right"><font face="Courier New">d</font><font face="Courier New" size="2">:</font></p>
573	</td>
574	<td>Dual constraint residuals</td>
575	</tr>
576	</table>
577	</td>
578	</tr>
579	<tr>
580	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
581	Description</th>
582	</tr>
583	<tr>
584	<td class="tabxpl">checkset is used to examine satisfaction of constraints
585	in a <a href="#set">set</a> object.</td>
586	</tr>
587	<tr>
588	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
589	Examples</th>
590	</tr>
591	<tr>
592	<td class="tabxpl"><p>After solving a problem, we can easily check how
593	well the constraints are satisfied.</p><table cellpadding="10" width="100%">
594	<tr>
595	<td class="xmpcode">
596	<pre>solvesdp(F,objective);
597	checkset(F)</pre>
598	</td>
599	</tr>
600	</table>
601	<p>The constraint residuals are defined as smallest eigenvalue, smallest
602	element, negated largest absolute-value element and largest distance
603	to an integer for semidefinite, element-wise, second order cone and
604	integrality constraints respectively. Hence, a solution is feasible
605	if all residuals related to inequalities are non-negative and residuals
606	related to equalities are sufficiently close to zero.</p>
607	<p>Sometimes it might be convenient to have the numerical values of
608	the constraint violations</p>
609	<table cellpadding="10" width="100%">
610	<tr>
611	<td class="xmpcode">
612	<pre>[p,d] = checkset(F);</pre>
613	</td>
614	</tr>
615	</table>
616	</td>
617	</tr>
618	<tr>
619	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
620	Related commands</th>
621	</tr>
622	<tr>
623	<td class="tabxpl"><a href="reference.htm#set">set</a>,
624	<a href="reference.htm#solvesdp">solvesdp</a></td>
625	</tr>
626	</table>
627	</td>
628	</tr>
629	</table>
630	<p class="Sh2"> </p>
631	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
632	<tr>
633	<td class="tableheader">
634	<p class="tableheader"><a name="clean">CLEAN</a></p>
635	</td>
636	</tr>
637	<tr>
638	<td>
639	<table cellspacing="0" cellpadding="4" width="100%" border="0">
640	<tr>
641	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
642	Syntax</th>
643	<td class="code" valign="top" nowrap width="100%"><code>y = clean(x,tol)</code></td>
644	</tr>
645	<tr>
646	<td class="tabxpl">
647	<table border="0">
648	<tr>
649	<td>
650	<p align="right"><font face="Courier New" size="2">y:</font></p>
651	</td>
652	<td>sdpvar object</td>
653	</tr>
654	<tr>
655	<td>
656	<p align="right"><font face="Courier New" size="2">x:</font></p>
657	</td>
658	<td>sdpvar object</td>
659	</tr>
660	<tr>
661	<td>
662	<p align="right"><font face="Courier New" size="2">tol:</font></p>
663	</td>
664	<td>double (tolerance)</td>
665	</tr>
666	</table>
667	</td>
668	</tr>
669	<tr>
670	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
671	Description</th>
672	</tr>
673	<tr>
674	<td class="tabxpl">clean is used to remove base matrices in an
675	<a href="reference.htm#sdpvar">sdpvar</a> object that are small (mainly
676	used together with <a href="reference.htm#solvesos">solvesos</a>)</td>
677	</tr>
678	<tr>
679	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
680	Examples</th>
681	</tr>
682	<tr>
683	<td class="tabxpl"><p>Removing nuisance variables</p><table cellpadding="10" width="100%">
684	<tr>
685	<td class="xmpcode">
686	<pre>x1 = sdpvar(n,1);
687	x2 = sdpvar(n,1);
688	x = x1+1e-8*x2;
689	y = clean(x,1e-6);
690	sdisplay(y)
691	<font color="#000000">ans
692	'x1'</font></pre>
693	</td>
694	</tr>
695	</table>
696	</td>
697	</tr>
698	<tr>
699	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
700	Related commands</th>
701	</tr>
702	<tr>
703	<td class="tabxpl"><a href="reference.htm#sos">sos</a>,
704	<a href="reference.htm#sdpvar">sdpvar</a></td>
705	</tr>
706	</table>
707	</td>
708	</tr>
709	</table>
710	<p> </p>
711	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table19">
712	<tr>
713	<td class="tableheader">
714	<p class="tableheader"><a name="coefficients">COEFFICIENTS</a></p>
715	</td>
716	</tr>
717	<tr>
718	<td>
719	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table20">
720	<tr>
721	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
722	Syntax<p> </p>
723	</th>
724	<td class="code" valign="top" nowrap width="100%"><code>[c,v] =
725	coefficients(p,x)</code></td>
726	</tr>
727	<tr>
728	<td class="tabxpl">
729	<table border="0" id="table21">
730	<tr>
731	<td>
732	<p align="right"><font face="Courier New">c</font><font face="Courier New" size="2">:</font></p>
733	</td>
734	<td>Coefficients (sdpvar object)</td>
735	</tr>
736	<tr>
737	<td>
738	<p align="right"><font face="Courier New" size="2">v:</font></p>
739	</td>
740	<td>Monomials (sdpvar object)</td>
741	</tr>
742	<tr>
743	<td>
744	<p align="right"><font face="Courier New" size="2">p:</font></p>
745	</td>
746	<td>Polynomials (sdpvar object)</td>
747	</tr>
748	<tr>
749	<td>
750	<p align="right"><font face="Courier New">x</font><font face="Courier New" size="2">:</font></p>
751	</td>
752	<td>Variables (sdpvar object)</td>
753	</tr>
754	</table>
755	</td>
756	</tr>
757	<tr>
758	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
759	Description</th>
760	</tr>
761	<tr>
762	<td class="tabxpl">coefficients is used to extract the
763	coefficients of a polynomials.</td>
764	</tr>
765	<tr>
766	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
767	Examples</th>
768	</tr>
769	<tr>
770	<td class="tabxpl">Define a polynomial in variables <b>x</b> and
771	<b>y</b>, with coefficients parameterized by <b>s</b> and <b>t</b>.<table cellpadding="10" width="100%" id="table22">
772	<tr>
773	<td class="xmpcode">
774	<pre>sdpvar x y s t
775	p = x^2+xy(s+t)+s^2+t^2;</pre>
776	</td>
777	</tr>
778	</table>
779	<p>The coefficients are easily recovered</p>
780	<table cellpadding="10" width="100%" id="table23">
781	<tr>
782	<td class="xmpcode">
783	<pre>c = coefficients(p,[x y]);
784	sdisplay(c)
785
786	<font color="#000000">ans =
787	's^2+t^2'
788	's+t'
789	'1'</font></pre>
790	</td>
791	</tr>
792	</table>
793	<p>By adding a second output, the monomial basis is returned also.</p>
794	<table cellpadding="10" width="100%" id="table24">
795	<tr>
796	<td class="xmpcode">
797	<pre>[c,v] = coefficients(p,[x y]);
798	sdisplay([c v])
799
800	<font color="#000000">ans =
801	's^2+t^2' '1'
802	's+t' 'xy'
803	'1' 'x^2'</font></pre>
804	<pre>p-c'*v
805
806	<font color="#000000">ans =
807	0</font></pre>
808	</td>
809	</tr>
810	</table>
811	<p>Of-course, we might just as well consider this to be a
812	polynomial in <b>s</b> and <b>t</b> with coefficients
813	parameterized by <b>x</b> and
814	<b>y</b>.<table cellpadding="10" width="100%" id="table25">
815	<tr>
816	<td class="xmpcode">
817	<pre>[c,v] = coefficients(p,[s t]);
818	sdisplay([c v])
819
820	<font color="#000000">ans =
821	'x^2' '1'
822	'xy' 't'
823	'1' 't^2'
824	'xy' 's'
825	'1' 's^2'</font></pre>
826	</td>
827	</tr>
828	</table>
829	</td>
830	</tr>
831	<tr>
832	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
833	Related commands</th>
834	</tr>
835	<tr>
836	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a></td>
837	</tr>
838	</table>
839	</td>
840	</tr>
841	</table>
842	<p> </p>
843	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
844	<tr>
845	<td class="tableheader">
846	<p class="tableheader"><a name="cone">CONE</a></p>
847	</td>
848	</tr>
849	<tr>
850	<td>
851	<table cellspacing="0" cellpadding="4" width="100%" border="0">
852	<tr>
853	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2"> <p> </p>
854	</th>
855	<td class="code" valign="top" nowrap width="100%"><code>c = cone(x,y)</code></td>
856	</tr>
857	<tr>
858	<td class="tabxpl">
859	<table border="0">
860	<tr>
861	<td>
862	<p align="right"><font face="Courier New" size="2">c:</font></p>
863	</td>
864	<td>sdpvar object (only useful in set object)</td>
865	</tr>
866	<tr>
867	<td>
868	<p align="right"><font face="Courier New" size="2">x:</font></p>
869	</td>
870	<td>sdpvar object (vector)</td>
871	</tr>
872	<tr>
873	<td>
874	<p align="right"><font face="Courier New" size="2">y:</font></p>
875	</td>
876	<td>sdpvar object (scalar)</td>
877	</tr>
878	</table>
879	</td>
880	</tr>
881	<tr>
882	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
883	Description</th>
884	</tr>
885	<tr>
886	<td class="tabxpl">cone is used to define the constraints <b>
887	<font face="Tahoma">\|\|x\|\|</font>≤<font face="Tahoma">y</font></b></td>
888	</tr>
889	<tr>
890	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
891	Examples</th>
892	</tr>
893	<tr>
894	<td class="tabxpl"><p>Constraining the Euclidean norm of a vector to
895	be less than 1 is done with</p><table cellpadding="10" width="100%">
896	<tr>
897	<td class="xmpcode">
898	<pre>x = sdpvar(n,1);
899	F = set(cone(x,1));</pre>
900	</td>
901	</tr>
902	</table>
903	<p>Of-course, arbitrary complicated constructs are possible, such
904	as constraining the norm of the diagonal to be less than the sum of
905	the off-diagonal terms in a matrix! </p>
906	<table cellpadding="10" width="100%">
907	<tr>
908	<td class="xmpcode">
909	<pre>x = sdpvar(n,n);
910	F = set(cone(diag(x),sum(sum(x-diag(diag(x))))))</pre>
911	</td>
912	</tr>
913	</table>
914	<p>An alternative is to use the nonlinear norm operator instead
915	(see the examples on <a href="extoperators.htm">nonlinear
916	operators</a> for details)</p>
917	<table cellpadding="10" width="100%">
918	<tr>
919	<td class="xmpcode">
920	<pre>x = sdpvar(n,n);
921	F = set(norm(diag(x)) < sum(sum(x-diag(diag(x)))))</pre>
922	</td>
923	</tr>
924	</table>
925	</td>
926	</tr>
927	<tr>
928	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
929	Related commands</th>
930	</tr>
931	<tr>
932	<td class="tabxpl"><a href="reference.htm#rcone">rcone</a>,
933	<a href="#set">set</a>, <a href="reference.htm#sdpvar">sdpvar</a></td>
934	</tr>
935	</table>
936	</td>
937	</tr>
938	</table>
939	<p> </p>
940	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
941	<tr>
942	<td class="tableheader">
943	<p class="tableheader"><a name="cut">CUT</a></p>
944	</td>
945	</tr>
946	<tr>
947	<td>
948	<table cellspacing="0" cellpadding="4" width="100%" border="0">
949	<tr>
950	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
951	Syntax<p> </p>
952	</th>
953	<td class="code" valign="top" nowrap width="100%"><code>F = cut(X,'tag')</code></td>
954	</tr>
955	<tr>
956	<td class="tabxpl">
957	<table border="0">
958	<tr>
959	<td>
960	<p align="right"><font face="Courier New" size="2">F:</font></p>
961	</td>
962	<td>set object</td>
963	</tr>
964	<tr>
965	<td>
966	<p align="right"><font face="Courier New" size="2">X:</font></p>
967	</td>
968	<td>sdpvar or constraint object, or string</td>
969	</tr>
970	<tr>
971	<td>
972	<p align="right"><font face="Courier New" size="2">'tag':</font></p>
973	</td>
974	<td>char</td>
975	</tr>
976	</table>
977	</td>
978	</tr>
979	<tr>
980	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
981	Description</th>
982	</tr>
983	<tr>
984	<td class="tabxpl">cut is used to define user-specified cuts for the
985	global BMI solver.</td>
986	</tr>
987	<tr>
988	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
989	Example</th>
990	</tr>
991	<tr>
992	<td class="tabxpl"><p>The result from this command is nothing but a
993	<a href="#set">set</a> object.</p>
994	<table cellpadding="10" width="100%">
995	<tr>
996	<td class="xmpcode">
997	<pre>P = sdpvar(2,2);
998	F = cut((P-eye(2))*(P-eye(2))>0);
999	<font color="#000000">+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
1000	\| ID\| Constraint\| Type\|
1001	+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
1002	\| #1\| Numeric value\| Matrix inequality (quadratic) 2x2\|
1003	+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++</font></pre>
1004	</td>
1005	</tr>
1006	</table>
1007	<p>The only difference is that this constraint will not be used in
1008	the upper bound problem in the branch & bound procudure. The constraint
1009	will thus only be used to improve the relaxations. See the examples
1010	in <a target="topic" href="globalbmi.htm">global solutions of bilinear
1011	programs</a>.</p>
1012	</td>
1013	</tr>
1014	<tr>
1015	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1016	Related commands</th>
1017	</tr>
1018	<tr>
1019	<td class="tabxpl"><a href="reference.htm#set">set</a></td>
1020	</tr>
1021	</table>
1022	</td>
1023	</tr>
1024	</table>
1025	<p> </p>
1026	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table69">
1027	<tr>
1028	<td class="tableheader">
1029	<p class="tableheader"><a name="dissect">DISSECT</a></p>
1030	</td>
1031	</tr>
1032	<tr>
1033	<td>
1034	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table70">
1035	<tr>
1036	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1037	Syntax<p> </p>
1038	</th>
1039	<td class="code" valign="top" nowrap width="100%"><code>F =
1040	dissect(X)</code></td>
1041	</tr>
1042	<tr>
1043	<td class="tabxpl">
1044	<table border="0" id="table71">
1045	<tr>
1046	<td>
1047	<p align="right"><font face="Courier New" size="2">F:</font></p>
1048	</td>
1049	<td>set object</td>
1050	</tr>
1051	<tr>
1052	<td>
1053	<p align="right"><font face="Courier New" size="2">X:</font></p>
1054	</td>
1055	<td>set object</td>
1056	</tr>
1057	</table>
1058	</td>
1059	</tr>
1060	<tr>
1061	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1062	Description</th>
1063	</tr>
1064	<tr>
1065	<td class="tabxpl">dissect can be used to transform extremely
1066	large sparse and structured SDP constraints to a set of smaller
1067	SDP constraints, at the price of introducing more variables.</td>
1068	</tr>
1069	<tr>
1070	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1071	Example</th>
1072	</tr>
1073	<tr>
1074	<td class="tabxpl">NOTE : For the examples below to work, you need
1075	to have
1076	<a target="_blank" href="http://www.cerfacs.fr/algor/Softs/MESHPART/">
1077	MESHPART</a> installed.
1078	<p>Let us begin by defining a large but low bandwidth SDP
1079	constraint.</p>
1080	<table cellpadding="10" width="100%" id="table72">
1081	<tr>
1082	<td class="xmpcode">
1083	<pre>n = 500;
1084	r = 3;
1085	B = randn(n,r+1);
1086	S = spdiags(B,0:r,n,n);S = S+S';
1087	x = sdpvar(n,1);
1088	X = diag(x)-S;
1089	p = randperm(n);
1090	X = X(p,p);
1091	F = set(X > 0)
1092	spy(F)<font color="#000000">
1093	+++++++++++++++++++++++++++++++++++++++++++++++++++++
1094	\| ID\| Constraint\| Type\|
1095	+++++++++++++++++++++++++++++++++++++++++++++++++++++
1096	\| #1\| Numeric value\| Matrix inequality 500x500\|
1097	+++++++++++++++++++++++++++++++++++++++++++++++++++++</font></pre>
1098	</td>
1099	</tr>
1100	</table>
1101	<p>Applying the dissect command simplifies the constraint to a set
1102	of two smaller SDP constraints, at the price of introducing 6
1103	additional variables.</p>
1104	<table cellpadding="10" width="100%" id="table73">
1105	<tr>
1106	<td class="xmpcode">
1107	<pre>dissect(F)
1108	<font color="#000000">+++++++++++++++++++++++++++++++++++++++++++++++++++++
1109	\| ID\| Constraint\| Type\|
1110	+++++++++++++++++++++++++++++++++++++++++++++++++++++
1111	\| #1\| Numeric value\| Matrix inequality 252x252\|
1112	\| #2\| Numeric value\| Matrix inequality 251x251\|
1113	+++++++++++++++++++++++++++++++++++++++++++++++++++++</font>
1114	length(getvariables(dissect(F)))
1115	<font color="#000000">ans =</font></pre>
1116	<pre><font color="#000000"> 506</font></pre>
1117	</td>
1118	</tr>
1119	</table>
1120	<p>The procedure can be recursively applied.</p>
1121	<table cellpadding="10" width="100%" id="table74">
1122	<tr>
1123	<td class="xmpcode">
1124	<pre>dissect(dissect(F))
1125	<font color="#000000">+++++++++++++++++++++++++++++++++++++++++++++++++++++
1126	\| ID\| Constraint\| Type\|
1127	+++++++++++++++++++++++++++++++++++++++++++++++++++++
1128	\| #1\| Numeric value\| Matrix inequality 128x128\|
1129	\| #2\| Numeric value\| Matrix inequality 127x127\|
1130	\| #3\| Numeric value\| Matrix inequality 127x127\|
1131	\| #4\| Numeric value\| Matrix inequality 127x127\|
1132	+++++++++++++++++++++++++++++++++++++++++++++++++++++</font>
1133	length(getvariables(dissect((dissect(F)))))
1134	<font color="#000000">ans =</font></pre>
1135	<pre><font color="#000000"> 518</font></pre>
1136	</td>
1137	</tr>
1138	</table>
1139	<p>To see the impact of the dissection, let us solve an SDP
1140	problem for various levels of dissection</p>
1141	<table cellpadding="10" width="100%" id="table75">
1142	<tr>
1143	<td class="xmpcode">
1144	<pre>sol = solvesdp(F,trace(X));sol.solvertime
1145	<font color="#000000">ans =</font></pre>
1146	<pre><font color="#000000"> 123.2810
1147
1148	</font>F = dissect(F);
1149	sol = solvesdp(F,trace(X));sol.solvertime
1150	<font color="#000000">ans =</font></pre>
1151	<pre><font color="#000000"> 36.0940
1152
1153	</font>F = dissect(F);
1154	sol = solvesdp(F,trace(X));sol.solvertime
1155	<font color="#000000">ans =</font></pre>
1156	<pre><font color="#000000"> 11.9070</font></pre>
1157	<pre>F = dissect(F);
1158	sol = solvesdp(F,trace(X));sol.solvertime
1159	<font color="#000000">ans =</font></pre>
1160	<pre><font color="#000000"> 4.6410</font></pre>
1161	<pre>F = dissect(F);
1162	sol = solvesdp(F,trace(X));sol.solvertime
1163	<font color="#000000">ans =</font></pre>
1164	<pre><font color="#000000"> 3.8430</font></pre>
1165	<pre>F = dissect(F);
1166	sol = solvesdp(F,trace(X));sol.solvertime
1167	<font color="#000000">ans =</font></pre>
1168	<pre><font color="#000000"> 3.9370</font></pre>
1169	</td>
1170	</tr>
1171	</table>
1172	<p>Note that the dissection command can be applied to arbitrary
1173	SDP problems in YALMIP (nonlinear problems, mixed semidefinite
1174	and second order cone problems etc).</p>
1175	<p>The algorithm in the command is based on finding a vertex
1176	separator of the matrix in the SDP constraint, applying a
1177	Dulmage-Mendelsohn permutation to detect corresponding blocks,
1178	followed by a series of Schur completions. Details will be available in an
1179	accompanying report soon...
1180	</td>
1181	</tr>
1182	<tr>
1183	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1184	Related commands</th>
1185	</tr>
1186	<tr>
1187	<td class="tabxpl"><a href="reference.htm#set">set</a>, <a href="reference.htm#unblkdiag">unblkdiag</a></td>
1188	</tr>
1189	</table>
1190	</td>
1191	</tr>
1192	</table>
1193	<p> </p>
1194	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
1195	<tr>
1196	<td class="tableheader">
1197	<p class="tableheader"><a name="double">DOUBLE</a></p>
1198	</td>
1199	</tr>
1200	<tr>
1201	<td>
1202	<table cellspacing="0" cellpadding="4" width="100%" border="0">
1203	<tr>
1204	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1205	Syntax</th>
1206	<td class="code" valign="top" nowrap width="100%"><code>Y = double(X)</code></td>
1207	</tr>
1208	<tr>
1209	<td class="tabxpl">
1210	<table border="0">
1211	<tr>
1212	<td>
1213	<p align="right"><font face="Courier New" size="2">Y:</font></p>
1214	</td>
1215	<td>double</td>
1216	</tr>
1217	<tr>
1218	<td>
1219	<p align="right"><font face="Courier New" size="2">X:</font></p>
1220	</td>
1221	<td>sdpvar or set object</td>
1222	</tr>
1223	</table>
1224	</td>
1225	</tr>
1226	<tr>
1227	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1228	Description</th>
1229	</tr>
1230	<tr>
1231	<td class="tabxpl">double is used to extract the numerical value of
1232	a decision variable, or the residual of a constraint</td>
1233	</tr>
1234	<tr>
1235	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1236	Examples</th>
1237	</tr>
1238	<tr>
1239	<td class="tabxpl"><p>After solving an optimization problem we might,
1240	e.g., extract the optimal objective value.</p><table cellpadding="10" width="100%">
1241	<tr>
1242	<td class="xmpcode">
1243	<pre>solvesdp(F,obj);
1244	optobj = double(obj);</pre>
1245	</td>
1246	</tr>
1247	</table>
1248	<p>It can also be used to extract the residual of a constraint </p>
1249	<table cellpadding="10" width="100%">
1250	<tr>
1251	<td class="xmpcode">
1252	<pre>solvesdp(F,obj);
1253	res = double(F(1));</pre>
1254	</td>
1255	</tr>
1256	</table>
1257	</td>
1258	</tr>
1259	<tr>
1260	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1261	Related commands</th>
1262	</tr>
1263	<tr>
1264	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>,
1265	<a href="reference.htm#solvesdp">solvesdp</a>,
1266	<a href="reference.htm#assign">assign</a></td>
1267	</tr>
1268	</table>
1269	</td>
1270	</tr>
1271	</table>
1272	<p> </p>
1273	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table76">
1274	<tr>
1275	<td class="tableheader">
1276	<p class="tableheader"><a name="hessian0">HESSIAN</a></p>
1277	</td>
1278	</tr>
1279	<tr>
1280	<td>
1281	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table77">
1282	<tr>
1283	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1284	Syntax</th>
1285	<td class="code" valign="top" nowrap width="100%"><code>H = hessian(f,x)</code></td>
1286	</tr>
1287	<tr>
1288	<td class="tabxpl">
1289	<table border="0" id="table78">
1290	<tr>
1291	<td>
1292	<p align="right"><font face="Courier New" size="2">H:</font></p>
1293	</td>
1294	<td>sdpvar object</td>
1295	</tr>
1296	<tr>
1297	<td>
1298	<p align="right"><font face="Courier New" size="2">f:</font></p>
1299	</td>
1300	<td>scalar sdpvar object </td>
1301	</tr>
1302	<tr>
1303	<td>
1304	<p align="right"><font face="Courier New" size="2">x:</font></p>
1305	</td>
1306	<td>sdpvar object</td>
1307	</tr>
1308	</table>
1309	</td>
1310	</tr>
1311	<tr>
1312	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1313	Description</th>
1314	</tr>
1315	<tr>
1316	<td class="tabxpl">Hessian calculates d2f/dx2</td>
1317	</tr>
1318	<tr>
1319	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1320	Examples</th>
1321	</tr>
1322	<tr>
1323	<td class="tabxpl">With only 1 argument, the differentiation is performed
1324	with respect to all involved variables<table cellpadding="10" width="100%" id="table79">
1325	<tr>
1326	<td class="xmpcode">
1327	<pre>x1 = sdpvar(1,1);
1328	x2 = sdpvar(1,1);
1329	f = x1^4+5*x2^2;
1330	sdisplay(hessian(f))</pre>
1331	<pre><font color="#000000">ans = </font></pre>
1332	<pre><font color="#000000"> '12x1^2' '0'
1333	'0'   '10'</font></pre>
1334	</td>
1335	</tr>
1336	</table>
1337	<p>Giving a second argument controls what variables to differentiate
1338	with respect to </p>
1339	<table cellpadding="10" width="100%" id="table80">
1340	<tr>
1341	<td class="xmpcode">
1342	<pre>sdisplay(hessian(f,x1))
1343	<font color="#000000">ans = </font></pre>
1344	<pre><font color="#000000"> '12x1^2'</font></pre>
1345	</td>
1346	</tr>
1347	</table>
1348	</td>
1349	</tr>
1350	<tr>
1351	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1352	Related commands</th>
1353	</tr>
1354	<tr>
1355	<td class="tabxpl"><a href="reference.htm#jacobian">jacobian</a>,
1356	<a href="reference.htm#sdisplay">sdisplay</a>,
1357	<a href="reference.htm#sdpvar">sdpvar</a></td>
1358	</tr>
1359	</table>
1360	</td>
1361	</tr>
1362	</table>
1363	<p> </p>
1364	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
1365	<tr>
1366	<td class="tableheader">
1367	<p class="tableheader"><a name="dual">DUAL</a></p>
1368	</td>
1369	</tr>
1370	<tr>
1371	<td>
1372	<table cellspacing="0" cellpadding="4" width="100%" border="0">
1373	<tr>
1374	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1375	Syntax</th>
1376	<td class="code" valign="top" nowrap width="100%"><code>Z = dual(F)</code></td>
1377	</tr>
1378	<tr>
1379	<td class="tabxpl">
1380	<table border="0">
1381	<tr>
1382	<td>
1383	<p align="right"><font face="Courier New" size="2">Z:</font></p>
1384	</td>
1385	<td>double</td>
1386	</tr>
1387	<tr>
1388	<td>
1389	<p align="right"><font face="Courier New" size="2">F:</font></p>
1390	</td>
1391	<td>set object (with one constraint)</td>
1392	</tr>
1393	</table>
1394	</td>
1395	</tr>
1396	<tr>
1397	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1398	Description</th>
1399	</tr>
1400	<tr>
1401	<td class="tabxpl">dual is used to extract the dual variable related
1402	to a constraint</td>
1403	</tr>
1404	<tr>
1405	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1406	Examples</th>
1407	</tr>
1408	<tr>
1409	<td class="tabxpl"><p>After solving an optimization problem we might,
1410	e.g., extract the dual variable of the 2nd constraint.</p><table cellpadding="10" width="100%">
1411	<tr>
1412	<td class="xmpcode">
1413	<pre>solvesdp(F,obj);
1414	Z2 = dual(F(2));</pre>
1415	</td>
1416	</tr>
1417	</table>
1418	<p>If the constraints in the set object have been tagged, we can use
1419	the tag instead </p>
1420	<table cellpadding="10" width="100%">
1421	<tr>
1422	<td class="xmpcode">
1423	<pre>solvesdp(F,obj);
1424	Z2 = dual(F('Lyapunov constraint'));</pre>
1425	</td>
1426	</tr>
1427	</table>
1428	</td>
1429	</tr>
1430	<tr>
1431	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1432	Related commands</th>
1433	</tr>
1434	<tr>
1435	<td class="tabxpl"><a href="reference.htm#set">set</a>,
1436	<a href="reference.htm#solvesdp">solvesdp</a>,
1437	<a href="reference.htm#sdpvar">sdpvar</a></td>
1438	</tr>
1439	</table>
1440	</td>
1441	</tr>
1442	</table>
1443	<p> </p>
1444	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
1445	<tr>
1446	<td class="tableheader">
1447	<p class="tableheader"><a name="dualize">DUALIZE</a></p>
1448	</td>
1449	</tr>
1450	<tr>
1451	<td>
1452	<table cellspacing="0" cellpadding="4" width="100%" border="0">
1453	<tr>
1454	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1455	Syntax</th>
1456	<td class="code" valign="top" nowrap width="100%"><code>
1457	[Fd,objd,X,free] = dualize(F,obj)</code></td>
1458	</tr>
1459	<tr>
1460	<td class="tabxpl">
1461	<table border="0">
1462	<tr>
1463	<td>
1464	<p align="right"><font face="Courier New" size="2">F:</font></p>
1465	</td>
1466	<td>set object in primal SDP form</td>
1467	</tr>
1468	<tr>
1469	<td>
1470	<p align="right"><font face="Courier New" size="2">obj:</font></p>
1471	</td>
1472	<td>sdpvar object (primal cost)</td>
1473	</tr>
1474	<tr>
1475	<td>
1476	<p align="right"><font face="Courier New" size="2">Fd:</font></p>
1477	</td>
1478	<td>set object in dual SDP form</td>
1479	</tr>
1480	<tr>
1481	<td>
1482	<p align="right"><font face="Courier New">objd</font><font face="Courier New" size="2">:</font></p>
1483	</td>
1484	<td>sdpvar object (dual cost)</td>
1485	</tr>
1486	<tr>
1487	<td>
1488	<p align="right"><font face="Courier New" size="2">X:</font></p>
1489	</td>
1490	<td>cell of sdpvar object (primal cone variables)</td>
1491	</tr>
1492	<tr>
1493	<td>
1494	<p align="right"><font face="Courier New" size="2">free:</font></p>
1495	</td>
1496	<td>sdpvar objects (free primal variables)</td>
1497	</tr>
1498	</table>
1499	</td>
1500	</tr>
1501	<tr>
1502	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1503	Description</th>
1504	</tr>
1505	<tr>
1506	<td class="tabxpl">dualize is used to convert a SDP problem given
1507	in primal form to the corresponding dual problem.</td>
1508	</tr>
1509	<tr>
1510	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1511	Examples</th>
1512	</tr>
1513	<tr>
1514	<td class="tabxpl">Consider the following SDP problem in primal
1515	form.<table cellpadding="10" width="100%">
1516	<tr>
1517	<td class="xmpcode">
1518	<pre>X = sdpvar(3,3);
1519	Y = sdpvar(3,3);
1520	F = set(X>0) + set(Y>0);
1521	F = F + set(X(1,3)==9) + set(Y(1,1)==X(2,2));
1522	F = F + set(sum(sum(X))+sum(sum(Y)) == 20);
1523	obj = trace(X)+trace(Y);</pre>
1524	</td>
1525	</tr>
1526	</table>
1527	<p>We can solve this in the given format. This will however be
1528	very inefficient in YALMIP, since the matrices X and Y will be
1529	explicitely parameterized, and the problem will be solved in a
1530	dual form with equality constraints. Instead, we note that the
1531	problem is an SDP in standard primal form. We therefor let YALMIP
1532	extract this primal model, and return the dual of this. If we
1533	solve this problem, the dual of this will be the original primal.
1534	Confused yet? (note that the dual objective should be maximized)</p>
1535	<table cellpadding="10" width="100%">
1536	<tr>
1537	<td class="xmpcode">
1538	<pre>[Fd,objd,XX,y] = dualize(F,obj);
1539	solvesdp(Fd,-objd);</pre>
1540	</td>
1541	</tr>
1542	</table>
1543	<p>To obtain our original variables, we extract the duals</p>
1544	<table cellpadding="10" width="100%">
1545	<tr>
1546	<td class="xmpcode">
1547	<pre>assign(XX{1},dual(Fd(1));
1548	assign(XX{2},dual(Fd(2));</pre>
1549	</td>
1550	</tr>
1551	</table>
1552	<p>Check out the tutorial for more <a href="dual.htm#dualize">
1553	examples</a></td>
1554	</tr>
1555	<tr>
1556	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1557	Related commands</th>
1558	</tr>
1559	<tr>
1560	<td class="tabxpl">
1561	<a href="reference.htm#dual">dual</a>,
1562	<a href="reference.htm#set">set</a>,
1563	<a href="reference.htm#solvesdp">solvesdp</a>,
1564	<a href="reference.htm#sdpvar">sdpvar</a></td>
1565	</tr>
1566	</table>
1567	</td>
1568	</tr>
1569	</table>
1570	<p> </p>
1571	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
1572	<tr>
1573	<td class="tableheader">
1574	<p class="tableheader"><a name="export">EXPORT</font></a></p>
1575	</td>
1576	</tr>
1577	<tr>
1578	<td>
1579	<table cellspacing="0" cellpadding="4" width="100%" border="0">
1580	<tr>
1581	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1582	Syntax<p> </p>
1583	</th>
1584	<td class="code" valign="top" nowrap width="100%"><code>[model,recoverymodel]
1585	= export(F,h,ops)</code></td>
1586	</tr>
1587	<tr>
1588	<td class="tabxpl">
1589	<table border="0">
1590	<tr>
1591	<td>
1592	<p align="right"><font face="Courier New" size="2">model:</font></p>
1593	</td>
1594	<td>Output structure.</td>
1595	</tr>
1596	<tr>
1597	<td>
1598	<font face="Courier New" size="2">recoverymodel:</font></td>
1599	<td>Output structure.</td>
1600	</tr>
1601	<tr>
1602	<td>
1603	<p align="right"><font face="Courier New" size="2">F:</font></p>
1604	</td>
1605	<td>set object describing the constraints. </td>
1606	</tr>
1607	<tr>
1608	<td>
1609	<p align="right"><font face="Courier New" size="2">h:</font></p>
1610	</td>
1611	<td>sdpvar-object describing the objective function.</td>
1612	</tr>
1613	<tr>
1614	<td>
1615	<p align="right"><font face="Courier New" size="2">ops:</font></p>
1616	</td>
1617	<td>options structure from sdpsettings.</td>
1618	</tr>
1619	</table>
1620	</td>
1621	</tr>
1622	<tr>
1623	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1624	Description</th>
1625	</tr>
1626	<tr>
1627	<td class="tabxpl">export is used to export YALMIP models to
1628	various solver formats (<font color="#FF0000">note : not all
1629	solvers are supported yet</font>)</td>
1630	</tr>
1631	<tr>
1632	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1633	Examples</th>
1634	</tr>
1635	<tr>
1636	<td class="tabxpl"><p>Consider a Lyapunov stability problem</p><table cellpadding="10" width="100%">
1637	<tr>
1638	<td class="xmpcode">
1639	<pre>A = randn(5,5);A = -A*A';
1640	P = sdpvar(5,5);
1641	F = set(A'P+PA < 0) + set(P>eye(5));
1642	obj = trace(P);</pre>
1643	</td>
1644	</tr>
1645	</table>
1646	<p>Exporting this to a model in SeDuMi format is done by
1647	specifying the solver as <code>'sedumi'</code> and calling export in the same way
1648	as <a href="reference.htm#solvesdp">solvesdp</a> would have ben called.</p>
1649	<table cellpadding="10" width="100%">
1650	<tr>
1651	<td class="xmpcode">
1652	<pre>[model,recoverymodel] = export(F,obj,sdpsettings('solver','sedumi'));</pre>
1653	<pre><font color="#000000">model = </font></pre>
1654	<pre><font color="#000000"> A: [50x15 double]
1655	b: [15x1 double]
1656	C: [50x1 double]
1657	K: [1x1 struct]
1658	pars: [1x1 struct]</font></pre>
1659	</td>
1660	</tr>
1661	</table>
1662	<p>The data in <code>recoverymodel</code> can be used to relate a solution
1663	obtained from using the exported model, to the actual variables in
1664	YALMIP. </p>
1665	<table cellpadding="10" width="100%">
1666	<tr>
1667	<td class="xmpcode">
1668	<pre>[x,y] = sedumi(model.A,model.b,model.C,model.K);
1669	assign(recover(recoverymodel.used_variables),y);</pre>
1670	</td>
1671	</tr>
1672	</table>
1673	<p>Some solvers do not support equality constraints. One way to
1674	handle this in YALMIP is to use <code>sdpsettings('remove',1)</code>.
1675	If this is done, YALMIP derives basis and
1676	solves the problem in the reduced variables. This basis is
1677	communicated through the structure <code>recoverymodel</code>.</p>
1678	<table cellpadding="10" width="100%">
1679	<tr>
1680	<td class="xmpcode">
1681	<pre>ops = sdpsettings('solver','sedumi','remove',1);
1682	[model,recoverymodel] = export(F+set(trace(P)==10),obj,ops);
1683	[x,y] = sedumi(model.A,model.b,model.C,model.K);
1684	z = recoverymodel.x_equ + recoverymodel.H*y;
1685	assign(recover(recoverymodel.used_variables),z);</pre>
1686	</td>
1687	</tr>
1688	</table>
1689	</td>
1690	</tr>
1691	<tr>
1692	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1693	Related commands</th>
1694	</tr>
1695	<tr>
1696	<td class="tabxpl"><a href="reference.htm#solvesdp">solvesdp</a></td>
1697	</tr>
1698	</table>
1699	</td>
1700	</tr>
1701	</table>
1702	<p> </p>
1703	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
1704	<tr>
1705	<td class="tableheader">
1706	<p class="tableheader"><a name="hessian">HESSIAN</a></p>
1707	</td>
1708	</tr>
1709	<tr>
1710	<td>
1711	<table cellspacing="0" cellpadding="4" width="100%" border="0">
1712	<tr>
1713	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1714	Syntax</th>
1715	<td class="code" valign="top" nowrap width="100%"><code>H = hessian(f,x)</code></td>
1716	</tr>
1717	<tr>
1718	<td class="tabxpl">
1719	<table border="0">
1720	<tr>
1721	<td>
1722	<p align="right"><font face="Courier New" size="2">H:</font></p>
1723	</td>
1724	<td>sdpvar object</td>
1725	</tr>
1726	<tr>
1727	<td>
1728	<p align="right"><font face="Courier New" size="2">f:</font></p>
1729	</td>
1730	<td>scalar sdpvar object </td>
1731	</tr>
1732	<tr>
1733	<td>
1734	<p align="right"><font face="Courier New" size="2">x:</font></p>
1735	</td>
1736	<td>sdpvar object</td>
1737	</tr>
1738	</table>
1739	</td>
1740	</tr>
1741	<tr>
1742	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1743	Description</th>
1744	</tr>
1745	<tr>
1746	<td class="tabxpl">Hessian calculates d2f/dx2</td>
1747	</tr>
1748	<tr>
1749	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1750	Examples</th>
1751	</tr>
1752	<tr>
1753	<td class="tabxpl">With only 1 argument, the differentiation is performed
1754	with respect to all involved variables<table cellpadding="10" width="100%">
1755	<tr>
1756	<td class="xmpcode">
1757	<pre>x1 = sdpvar(1,1);
1758	x2 = sdpvar(1,1);
1759	f = x1^4+5*x2^2;
1760	sdisplay(hessian(f))</pre>
1761	<pre><font color="#000000">ans = </font></pre>
1762	<pre><font color="#000000"> '12x1^2' '0'
1763	'0'   '10'</font></pre>
1764	</td>
1765	</tr>
1766	</table>
1767	<p>Giving a second argument controls what variables to differentiate
1768	with respect to </p>
1769	<table cellpadding="10" width="100%">
1770	<tr>
1771	<td class="xmpcode">
1772	<pre>sdisplay(hessian(f,x1))
1773	<font color="#000000">ans = </font></pre>
1774	<pre><font color="#000000"> '12x1^2'</font></pre>
1775	</td>
1776	</tr>
1777	</table>
1778	</td>
1779	</tr>
1780	<tr>
1781	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1782	Related commands</th>
1783	</tr>
1784	<tr>
1785	<td class="tabxpl"><a href="reference.htm#jacobian">jacobian</a>,
1786	<a href="reference.htm#sdisplay">sdisplay</a>,
1787	<a href="reference.htm#sdpvar">sdpvar</a></td>
1788	</tr>
1789	</table>
1790	</td>
1791	</tr>
1792	</table>
1793	<p> </p>
1794	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table132">
1795	<tr>
1796	<td class="tableheader">
1797	<p class="tableheader"><a name="hull">HULL</a></p>
1798	</td>
1799	</tr>
1800	<tr>
1801	<td>
1802	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table133">
1803	<tr>
1804	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1805	Syntax</th>
1806	<td class="code" valign="top" nowrap width="100%"><code>F = hull(F1,F2,...)</code></td>
1807	</tr>
1808	<tr>
1809	<td class="tabxpl">
1810	<table border="0" id="table134">
1811	<tr>
1812	<td>
1813	<p align="right"><font face="Courier New">F</font><font face="Courier New" size="2">:</font></p>
1814	</td>
1815	<td>set object </td>
1816	</tr>
1817	<tr>
1818	<td>
1819	<p align="right"><font face="Courier New" size="2">Fi:</font></p>
1820	</td>
1821	<td>set objects</td>
1822	</tr>
1823	</table>
1824	</td>
1825	</tr>
1826	<tr>
1827	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1828	Description</th>
1829	</tr>
1830	<tr>
1831	<td class="tabxpl">hull is used to create a convex representation
1832	of the convex hull of a set of constraints.</td>
1833	</tr>
1834	<tr>
1835	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1836	Examples</th>
1837	</tr>
1838	<tr>
1839	<td class="tabxpl">Define two polytope<table cellpadding="10" width="100%" id="table135">
1840	<tr>
1841	<td class="xmpcode">
1842	<pre>sdpvar x y
1843	F1 = set(-1 < x < 1) + set(-1 < y < 1);
1844	F2 = set(-1.5 < x-y < 1.5) + set(-1.5 < x+y < 1.5);</pre>
1845	</td>
1846	</tr>
1847	</table>
1848	<p>Plot the polytopes</p>
1849	<table cellpadding="10" width="100%" id="table136">
1850	<tr>
1851	<td class="xmpcode">
1852	<pre>plot(F2);hold on
1853	plot(F1);</pre>
1854	</td>
1855	</tr>
1856	</table>
1857	<p>Notice, if you have MPT installed, this is quicker</p>
1858	<table cellpadding="10" width="100%" id="table137">
1859	<tr>
1860	<td class="xmpcode">
1861	<pre>plot(polytope(F2));hold on
1862	plot(polytope(F1));</pre>
1863	</td>
1864	</tr>
1865	</table>
1866	<p>Create a convex model of the convex hull</p>
1867	<table cellpadding="10" width="100%" id="table138">
1868	<tr>
1869	<td class="xmpcode">
1870	<pre>H = hull(F1,F2)
1871	+++++++++++++++++++++++++++++++++++++++++++++++++++
1872	\| ID\| Constraint\| Type\|
1873	+++++++++++++++++++++++++++++++++++++++++++++++++++
1874	\| #1\| Numeric value\| Element-wise 2x1\|
1875	\| #2\| Numeric value\| Element-wise 2x1\|
1876	\| #3\| Numeric value\| Element-wise 2x1\|
1877	\| #4\| Numeric value\| Element-wise 2x1\|
1878	\| #5\| Numeric value\| Equality constraint 2x1\|
1879	\| #6\| Numeric value\| Equality constraint 1x1\|
1880	\| #7\| Numeric value\| Element-wise 2x1\|
1881	+++++++++++++++++++++++++++++++++++++++++++++++++++</pre>
1882	</td>
1883	</tr>
1884	</table>
1885	<p>Important to realize is that the representation will introduce
1886	new variables due to a lifting procedure. We can plot the convex hull, but since
1887	we have introduced new variables, we must declare that we
1888	are interested in the projection on the original variables <b>x</b>
1889	and <b>y</b></p>
1890	<table cellpadding="10" width="100%" id="table139">
1891	<tr>
1892	<td class="xmpcode">
1893	<pre>clf;
1894	plot(H,[x y]);hold on
1895	plot(F2);
1896	plot(F1);</pre>
1897	</td>
1898	</tr>
1899	</table>
1900	<p>The command applies to (almost) arbitrary convex constraints.<table cellpadding="10" width="100%" id="table140">
1901	<tr>
1902	<td class="xmpcode">
1903	<pre>clf;
1904	sdpvar x y
1905	F1 = set([1 x y+3;[x;y+3] 1/5*eye(2)] > 0);
1906	F2 = set(-1.5 < x-y < 1.5) + set(-1.5 < x+y < 1.5);
1907	H = hull(F1,F2);
1908	plot(H,[x y]);hold on
1909	plot(F2);
1910	plot(F1);</pre>
1911	</td>
1912	</tr>
1913	</table>
1914	<p>At the moment, the command does not support constraints that
1915	involve <a href="extoperators.htm">nonlinear operators</a> or
1916	quadratic terms, although this easily can be added if anyone
1917	needs it.</td>
1918	</tr>
1919	<tr>
1920	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1921	Related commands</th>
1922	</tr>
1923	<tr>
1924	<td class="tabxpl"><a href="reference.htm#set">set</a>,
1925	<a href="reference.htm#solvesdp">solvesdp</a>,
1926	<a href="reference.htm#sdpvar">sdpvar</a></td>
1927	</tr>
1928	</table>
1929	</td>
1930	</tr>
1931	</table>
1932	<p> </p>
1933	<p> </p>
1934	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table4">
1935	<tr>
1936	<td class="tableheader">
1937	<p class="tableheader"><a name="imagemodel">IMAGEMODEL</a></p>
1938	</td>
1939	</tr>
1940	<tr>
1941	<td>
1942	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table5">
1943	<tr>
1944	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1945	Syntax</th>
1946	<td class="code" valign="top" nowrap width="100%"><code>
1947	[Fi,obji,x,y] = imagemodel(F,obj)</code></td>
1948	</tr>
1949	<tr>
1950	<td class="tabxpl">
1951	<table border="0" id="table6">
1952	<tr>
1953	<td>
1954	<p align="right"><font face="Courier New" size="2">F:</font></p>
1955	</td>
1956	<td>set object</td>
1957	</tr>
1958	<tr>
1959	<td>
1960	<p align="right"><font face="Courier New" size="2">obj:</font></p>
1961	</td>
1962	<td>sdpvar object (objective)</td>
1963	</tr>
1964	<tr>
1965	<td>
1966	<p align="right"><font face="Courier New" size="2">Fd:</font></p>
1967	</td>
1968	<td>set object</td>
1969	</tr>
1970	<tr>
1971	<td>
1972	<p align="right"><font face="Courier New">obji</font><font face="Courier New" size="2">:</font></p>
1973	</td>
1974	<td>sdpvar object (dual cost)</td>
1975	</tr>
1976	<tr>
1977	<td>
1978	<p align="right"><font face="Courier New">x</font><font face="Courier New" size="2">:</font></p>
1979	</td>
1980	<td>sdpvar object  (original variables)</td>
1981	</tr>
1982	<tr>
1983	<td>
1984	<p align="right"><font face="Courier New">y</font><font face="Courier New" size="2">:</font></p>
1985	</td>
1986	<td>sdpvar object  (original variables expressed in new
1987	basis)</td>
1988	</tr>
1989	</table>
1990	</td>
1991	</tr>
1992	<tr>
1993	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
1994	Description</th>
1995	</tr>
1996	<tr>
1997	<td class="tabxpl">imagemodel is used to reduce the number of
1998	variables in a problem by eliminating explicit equality
1999	constraints</td>
2000	</tr>
2001	<tr>
2002	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2003	Examples</th>
2004	</tr>
2005	<tr>
2006	<td class="tabxpl">Consider the following equality constrained
2007	SDP.<table cellpadding="10" width="100%" id="table7">
2008	<tr>
2009	<td class="xmpcode">
2010	<pre>C = eye(2);
2011	A1 = randn(2,2);A1 = A1*A1';
2012	A2 = randn(2,2);A2 = A2*A2';
2013	A3 = randn(2,2);A3 = A3*A3';
2014	z = sdpvar(3,1);</pre>
2015	<pre>obj = sum(z)
2016	F = set(C+A1z(1)+A2z(2)+A3*z(3) > 0) + set(z(1)+z(2)== 1)</pre>
2017	</td>
2018	</tr>
2019	</table>
2020	<p>A model without the explicit equality constraint is easily
2021	obtained.</p>
2022	<table cellpadding="10" width="100%" id="table8">
2023	<tr>
2024	<td class="xmpcode">
2025	<pre>[Fi,obji,x,y] = imagemodel(F,obj);</pre>
2026	</td>
2027	</tr>
2028	</table>
2029	<p>We solve the reduced problem, and recover the original
2030	variables</p>
2031	<table cellpadding="10" width="100%" id="table9">
2032	<tr>
2033	<td class="xmpcode">
2034	<pre>solvesdp(F,obji);
2035	assign(x,double(y));</pre>
2036	</td>
2037	</tr>
2038	</table>
2039	<p>Note that this reduction is automatically done when you call
2040	<a href="reference.htm#solvesdp">solvesdp</a> and use a solver
2041	that cannot handle equality constraints. Hence, there is
2042	typically no reason to use this command, unless some further
2043	manipulations are going to be performed.</td>
2044	</tr>
2045	<tr>
2046	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2047	Related commands</th>
2048	</tr>
2049	<tr>
2050	<td class="tabxpl">
2051	<a href="reference.htm#solvesdp">solvesdp</a>,
2052	<a href="reference.htm#sdpvar">sdpvar</a></td>
2053	</tr>
2054	</table>
2055	</td>
2056	</tr>
2057	</table>
2058	<p> </p>
2059	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
2060	<tr>
2061	<td class="tableheader">
2062	<p class="tableheader"><a name="integer">INTEGER</a></p>
2063	</td>
2064	</tr>
2065	<tr>
2066	<td>
2067	<table cellspacing="0" cellpadding="4" width="100%" border="0">
2068	<tr>
2069	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2070	Syntax</th>
2071	<td class="code" valign="top" nowrap width="100%"><code>c = integer(x)</code></td>
2072	</tr>
2073	<tr>
2074	<td class="tabxpl">
2075	<table border="0">
2076	<tr>
2077	<td>
2078	<p align="right"><font face="Courier New" size="2">c:</font></p>
2079	</td>
2080	<td>sdpvar object (only useful in set object)</td>
2081	</tr>
2082	<tr>
2083	<td>
2084	<p align="right"><font face="Courier New" size="2">x:</font></p>
2085	</td>
2086	<td>sdpvar object</td>
2087	</tr>
2088	</table>
2089	</td>
2090	</tr>
2091	<tr>
2092	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2093	Description</th>
2094	</tr>
2095	<tr>
2096	<td class="tabxpl">integer is used to constrain a set of variable
2097	to be integer.</td>
2098	</tr>
2099	<tr>
2100	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2101	Examples</th>
2102	</tr>
2103	<tr>
2104	<td class="tabxpl">Setting up a integer linear program {<b><font face="Tahoma">min
2105	c<sup>T</sup>x subject to Ax</font>≤<font face="Tahoma">b</font></b>}
2106	can be done as<table cellpadding="10" width="100%">
2107	<tr>
2108	<td class="xmpcode">
2109	<pre>x = intvar(n,1);
2110	solvesdp(set(Ax<b),c'x)</pre>
2111	</td>
2112	</tr>
2113	</table>
2114	<p>or </p>
2115	<table cellpadding="10" width="100%">
2116	<tr>
2117	<td class="xmpcode">
2118	<pre> </pre>
2119	<pre>x = sdpvar(n,1);
2120	solvesdp(set(Ax<b)+set(integer(x),c'x)</pre>
2121	</td>
2122	</tr>
2123	</table>
2124	<p>Note, the integrality constraint is imposed on the involved variables,
2125	not the actual <a href="#sdpvar">sdpvar</a> object. Hence, the following
2126	two constraints are equivalent </p>
2127	<table cellpadding="10" width="100%">
2128	<tr>
2129	<td class="xmpcode">
2130	<pre>F = set(integer(x));
2131	F = set(integer(pi+sqrt(2)*x));</pre>
2132	</td>
2133	</tr>
2134	</table>
2135	</td>
2136	</tr>
2137	<tr>
2138	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2139	Related commands</th>
2140	</tr>
2141	<tr>
2142	<td class="tabxpl"><a href="reference.htm#intvar">intvar</a>,
2143	<a href="reference.htm#sdpvar">sdpvar</a>,
2144	<a href="reference.htm#binvar">binvar</a>, <a href="#set">set</a></td>
2145	</tr>
2146	</table>
2147	</td>
2148	</tr>
2149	</table>
2150	<p> </p>
2151	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
2152	<tr>
2153	<td class="tableheader">
2154	<p class="tableheader"><a name="intvar">INTVAR</a></p>
2155	</td>
2156	</tr>
2157	<tr>
2158	<td>
2159	<table cellspacing="0" cellpadding="4" width="100%" border="0">
2160	<tr>
2161	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2162	Syntax </th>
2163	<td class="code" valign="top" nowrap width="100%"><code>x = intvar(n,m,'field','type')</code></td>
2164	</tr>
2165	<tr>
2166	<td class="tabxpl">
2167	<table border="0">
2168	<tr>
2169	<td>
2170	<p align="right"><font face="Courier New" size="2">n:</font></p>
2171	</td>
2172	<td>Height</td>
2173	</tr>
2174	<tr>
2175	<td>
2176	<p align="right"><font face="Courier New" size="2">m:</font></p>
2177	</td>
2178	<td>Width</td>
2179	</tr>
2180	<tr>
2181	<td>
2182	<p align="right"><font face="Courier New" size="2">'field':</font></p>
2183	</td>
2184	<td>char {'real','complex'}</td>
2185	</tr>
2186	<tr>
2187	<td>
2188	<p align="right"><font face="Courier New" size="2">'type':</font></p>
2189	</td>
2190	<td>char {'symmetric','full','hermitian','toeplitz','hankel','skew'}</td>
2191	</tr>
2192	</table>
2193	</td>
2194	</tr>
2195	<tr>
2196	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2197	Description</th>
2198	</tr>
2199	<tr>
2200	<td class="tabxpl">intvar is used to define symbolic decision variables
2201	with integer elements.</td>
2202	</tr>
2203	<tr>
2204	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2205	Examples</th>
2206	</tr>
2207	<tr>
2208	<td class="tabxpl">A scalar integer variable is defined with<table cellpadding="10" width="100%">
2209	<tr>
2210	<td class="xmpcode">
2211	<pre>P = intvar(1,1)</pre>
2212	</td>
2213	</tr>
2214	</table>
2215	<p>For more examples, see <a href="reference.htm#sdpvar">sdpvar</a>.</p>
2216	</td>
2217	</tr>
2218	<tr>
2219	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2220	Related commands</th>
2221	</tr>
2222	<tr>
2223	<td class="tabxpl"><a href="reference.htm#binvar">binvar</a>,
2224	<a href="reference.htm#sdpvar">sdpvar</a>,
2225	<a href="reference.htm#integer">integer</a>,
2226	<a href="reference.htm#binary">binary</a>, <a href="#set">set</a></td>
2227	</tr>
2228	</table>
2229	</td>
2230	</tr>
2231	</table>
2232	<p> </p>
2233	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
2234	<tr>
2235	<td class="tableheader">
2236	<p class="tableheader"><a name="is">IS</a></p>
2237	</td>
2238	</tr>
2239	<tr>
2240	<td>
2241	<table cellspacing="0" cellpadding="4" width="100%" border="0">
2242	<tr>
2243	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2244	Syntax</th>
2245	<td class="code" valign="top" nowrap width="100%"><code>y = is(x,'property')</code></td>
2246	</tr>
2247	<tr>
2248	<td class="tabxpl">
2249	<table border="0">
2250	<tr>
2251	<td>
2252	<p align="right"><font face="Courier New" size="2">y:</font></p>
2253	</td>
2254	<td>logical</td>
2255	</tr>
2256	<tr>
2257	<td>
2258	<p align="right"><font face="Courier New" size="2">x:</font></p>
2259	</td>
2260	<td>sdpvar or set object </td>
2261	</tr>
2262	<tr>
2263	<td>
2264	<p align="right"><font face="Courier New">property</font><font face="Courier New" size="2">:</font></p>
2265	</td>
2266	<td>char {'real', 'symmetric', 'hermitian', 'scalar', 'linear',
2267	'homogeneous', 'integer', 'binary'}  for sdpvar  objects,
2268	{'elementwise', 'socc','lmi', 'linear', 'kyp'} on set objects</td>
2269	</tr>
2270	</table>
2271	</td>
2272	</tr>
2273	<tr>
2274	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2275	Description</th>
2276	</tr>
2277	<tr>
2278	<td class="tabxpl">is is used to check properties of sdpvar and set
2279	objects.</td>
2280	</tr>
2281	<tr>
2282	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2283	Examples</th>
2284	</tr>
2285	<tr>
2286	<td class="tabxpl">Checking if an <a href="reference.htm#sdpvar">sdpvar</a>
2287	object is linear can be done with is<table cellpadding="10" width="100%">
2288	<tr>
2289	<td class="xmpcode">
2290	<pre>x = sdpvar(1,1);
2291	y = [x;x*x];
2292	is(y,'linear')
2293	<font color="#000000">ans =
2294	0</font></pre>
2295	</td>
2296	</tr>
2297	</table>
2298	<p>The command works almost in the same way on <a href="#set">set
2299	</a>objects, with the difference that the check is performed on every
2300	constraint in the <a href="reference.htm#set">set</a> object separately,
2301	so the output can be a vector </p>
2302	<table cellpadding="10" width="100%">
2303	<tr>
2304	<td class="xmpcode">
2305	<pre>x = sdpvar(1,1);
2306	F = set(x>1) + set([1 x;x 1]>0) + set(x<3);
2307	is(F,'elementwise')
2308	<font color="#000000">ans =</font></pre>
2309	<pre><font color="#000000"> 1
2310	0
2311	1</font></pre>
2312	</td>
2313	</tr>
2314	</table>
2315	<p>Hence, creating a <a href="#set">set</a> object containing only
2316	the element-wise constraints is done with </p>
2317	<table cellpadding="10" width="100%">
2318	<tr>
2319	<td class="xmpcode">
2320	<pre>F_element = F(is(F,'elementwise'));</pre>
2321	</td>
2322	</tr>
2323	</table>
2324	</td>
2325	</tr>
2326	<tr>
2327	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2328	Related commands</th>
2329	</tr>
2330	<tr>
2331	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>,
2332	<a href="#set">set</a></td>
2333	</tr>
2334	</table>
2335	</td>
2336	</tr>
2337	</table>
2338	<p> </p>
2339	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table112">
2340	<tr>
2341	<td class="tableheader">
2342	<p class="tableheader"><a name="ismember">ISMEMBER</font></a></p>
2343	</td>
2344	</tr>
2345	<tr>
2346	<td>
2347	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table113">
2348	<tr>
2349	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2350	Syntax</th>
2351	<td class="code" valign="top" nowrap width="100%"><code>F =
2352	ismember(x,Y)</code></td>
2353	</tr>
2354	<tr>
2355	<td class="tabxpl">
2356	<table border="0" id="table114">
2357	<tr>
2358	<td>
2359	<p align="right"><font face="Courier New">F</font><font face="Courier New" size="2">:</font></p>
2360	</td>
2361	<td>set object</td>
2362	</tr>
2363	<tr>
2364	<td>
2365	<p align="right"><font face="Courier New" size="2">x:</font></p>
2366	</td>
2367	<td>sdpvar object</td>
2368	</tr>
2369	<tr>
2370	<td>
2371	<p align="right"><font face="Courier New" size="2">Y:</font></p>
2372	</td>
2373	<td>vector of doubles or polytope array</td>
2374	</tr>
2375	</table>
2376	</td>
2377	</tr>
2378	<tr>
2379	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2380	Description</th>
2381	</tr>
2382	<tr>
2383	<td class="tabxpl" height="26"><a href="#ismember">ismember</a> is used to constrain an sdpvar object to be part
2384	of a set of doubles or polytopes</td>
2385	</tr>
2386	<tr>
2387	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2388	Examples</th>
2389	</tr>
2390	<tr>
2391	<td class="tabxpl">To constrain a scalar variable to take a value
2392	from a finite set, <a href="#ismember">ismember</a> can be used.<table cellpadding="10" width="100%" id="table115">
2393	<tr>
2394	<td class="xmpcode">
2395	<pre>sdpvar x
2396	F = set(ismember(x,[1 2 3 4]));</pre>
2397	</td>
2398	</tr>
2399	</table>
2400	<p>Of course, this can also be obtained with a standard integer
2401	variable.</p><table cellpadding="10" width="100%" id="table116">
2402	<tr>
2403	<td class="xmpcode">
2404	<pre>intvar x
2405	F = set(1 <= x <=4);</pre>
2406	</td>
2407	</tr>
2408	</table>
2409	<p>or an integrality constraint</p>
2410	<table cellpadding="10" width="100%" id="table117">
2411	<tr>
2412	<td class="xmpcode">
2413	<pre>sdpvar x
2414	F = set(integer(x)) + set(1 <= x <= 4);</pre>
2415	</td>
2416	</tr>
2417	</table>
2418	<p>The functionality is more useful when the set is more
2419	complicated.</p>
2420	<table cellpadding="10" width="100%" id="table121">
2421	<tr>
2422	<td class="xmpcode">
2423	<pre>sdpvar x
2424	F = set(ismember(x,[1 pi 12 -8]));</pre>
2425	</td>
2426	</tr>
2427	</table>
2428	<p>The function <a href="#ismember">ismember</a> can also be used together with the
2429	polytope object in <a href="solvers.htm#mpt">MPT</a> to constrain a variable to be inside
2430	at least one
2431	of several polytopes.</p>
2432	<table cellpadding="10" width="100%" id="table122">
2433	<tr>
2434	<td class="xmpcode">
2435	<pre>x = sdpvar(3,1);
2436	P1 = polytope(randn(10,3),rand(10,1));
2437	P2 = polytope(randn(10,3),rand(10,1));
2438	F = set(ismember(x,[P1 P2]));</pre>
2439	</td>
2440	</tr>
2441	</table>
2442	<p>Note that <a href="#ismember">ismember</a> will introduce binary variables if the
2443	cardinality of the set <b>Y</b> is larger than 1</td>
2444	</tr>
2445	<tr>
2446	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2447	Related commands</th>
2448	</tr>
2449	<tr>
2450	<td class="tabxpl"><a href="reference.htm#set">set</a></td>
2451	</tr>
2452	</table>
2453
2454	</td>
2455	</tr>
2456	</table>
2457	<p> </p>
2458	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
2459	<tr>
2460	<td class="tableheader">
2461	<p class="tableheader"><a name="jacobian">JACOBIAN</a></p>
2462	</td>
2463	</tr>
2464	<tr>
2465	<td>
2466	<table cellspacing="0" cellpadding="4" width="100%" border="0">
2467	<tr>
2468	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2469	Syntax</th>
2470	<td class="code" valign="top" nowrap width="100%"><code>J = jacobian(f,x)</code></td>
2471	</tr>
2472	<tr>
2473	<td class="tabxpl">
2474	<table border="0">
2475	<tr>
2476	<td>
2477	<p align="right"><font face="Courier New" size="2">J:</font></p>
2478	</td>
2479	<td>sdpvar object</td>
2480	</tr>
2481	<tr>
2482	<td>
2483	<p align="right"><font face="Courier New" size="2">f:</font></p>
2484	</td>
2485	<td>sdpvar object </td>
2486	</tr>
2487	<tr>
2488	<td>
2489	<p align="right"><font face="Courier New" size="2">x:</font></p>
2490	</td>
2491	<td>sdpvar object</td>
2492	</tr>
2493	</table>
2494	</td>
2495	</tr>
2496	<tr>
2497	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2498	Description</th>
2499	</tr>
2500	<tr>
2501	<td class="tabxpl">jacobian calculates the Jacobian df/dx.</td>
2502	</tr>
2503	<tr>
2504	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2505	Examples</th>
2506	</tr>
2507	<tr>
2508	<td class="tabxpl">With only 1 argument, the differentiation is performed
2509	with respect to all involved variables (more precisely, with respect
2510	to the variables <a href="reference.htm#recover">recover</a>(<a href="reference.htm#depends">depends</a>(f)))<table cellpadding="10" width="100%">
2511	<tr>
2512	<td class="xmpcode">
2513	<pre>x1 = sdpvar(1,1);
2514	x2 = sdpvar(1,1);
2515	f = x1^2+5*x2^2;
2516	sdisplay(jacobian(f))</pre>
2517	<pre><font color="#000000">ans = </font></pre>
2518	<pre><font color="#000000"> '2x1' '10x2'</font></pre>
2519	</td>
2520	</tr>
2521	</table>
2522	<p>Giving a second argument controls what variables to differentiate
2523	with respect to </p>
2524	<table cellpadding="10" width="100%">
2525	<tr>
2526	<td class="xmpcode">
2527	<pre>sdisplay(jacobian(f,x2))
2528	<font color="#000000">ans = </font></pre>
2529	<pre><font color="#000000"> '10x2'</font></pre>
2530	</td>
2531	</tr>
2532	</table>
2533	</td>
2534	</tr>
2535	<tr>
2536	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2537	Related commands</th>
2538	</tr>
2539	<tr>
2540	<td class="tabxpl"><a href="reference.htm#hessian">hessian</a>,
2541	<a href="reference.htm#sdisplay">sdisplay</a>,
2542	<a href="reference.htm#sdpvar">sdpvar</a></td>
2543	</tr>
2544	</table>
2545	</td>
2546	</tr>
2547	</table>
2548	<p> </p>
2549	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
2550	<tr>
2551	<td class="tableheader">
2552	<p class="tableheader"><a name="kyp">KYP</a></p>
2553	</td>
2554	</tr>
2555	<tr>
2556	<td>
2557	<table cellspacing="0" cellpadding="4" width="100%" border="0">
2558	<tr>
2559	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2560	Syntax</th>
2561	<td class="code" valign="top" nowrap width="100%"><code>x = kyp(A,B,P,M)</code></td>
2562	</tr>
2563	<tr>
2564	<td class="tabxpl">
2565	<table border="0" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" cellspacing="0">
2566	<tr>
2567	<td>
2568	<p align="right"><font face="Courier New" size="2">x:</font></p>
2569	</td>
2570	<td>sdpvar object (only useful in set)</td>
2571	</tr>
2572	<tr>
2573	<td>
2574	<p align="right"><font face="Courier New" size="2">A:</font></p>
2575	</td>
2576	<td>double (square matrix)</td>
2577	</tr>
2578	<tr>
2579	<td>
2580	<p align="right"><font face="Courier New" size="2">B:</font></p>
2581	</td>
2582	<td>double</td>
2583	</tr>
2584	<tr>
2585	<td>
2586	<p align="right"><font face="Courier New" size="2">P:</font></p>
2587	</td>
2588	<td>sdpvar object (symmetric)</td>
2589	</tr>
2590	<tr>
2591	<td>
2592	<p align="right"><font face="Courier New" size="2">M:</font></p>
2593	</td>
2594	<td>sdpvar object (symmetric)</td>
2595	</tr>
2596	</table>
2597	</td>
2598	</tr>
2599	<tr>
2600	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2601	Description</th>
2602	</tr>
2603	<tr>
2604	<td class="tabxpl">kyp is used to define LMIs related to the KYP-lemma
2605	and Lyapunov equations</td>
2606	</tr>
2607	<tr>
2608	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2609	Examples</th>
2610	</tr>
2611	<tr>
2612	<td class="tabxpl">Defining the Lyapunov constraint <b>
2613	<font face="Tahoma">A<sup>T</sup>P+PA<0</font></b> can be done using
2614	<a href="reference.htm#kyp">kyp</a><table cellpadding="10" width="100%">
2615	<tr>
2616	<td class="xmpcode">
2617	<pre>F = set(kyp(A,[],P) < 0)</pre>
2618	</td>
2619	</tr>
2620	</table>
2621	<p>Tthe following command is equivalent </p>
2622	<table cellpadding="10" width="100%">
2623	<tr>
2624	<td class="xmpcode">
2625	<pre>F = set(A'P+PA < 0)</pre>
2626	</td>
2627	</tr>
2628	</table>
2629	<p>but the difference is that YALMIP does not know that the constraint
2630	is a Lyapunov equation, hence it will not be able to use the dedicated
2631	solver <a href="solvers.htm#kypd">KYPD</a>.<br />
2632	<br />
2633	<a href="reference.htm#kyp">kyp </a>can also be used to define more
2634	complex constraints. The following two commands generate the constraint
2635	<b><font face="Tahoma">[A<sup>T</sup>P+PA PB;B<sup>T</sup>P 0] + M(x)
2636	< 0 </font></b>(<b>P</b> and <b>x</b> are decision variables). </p>
2637	<table cellpadding="10" width="100%">
2638	<tr>
2639	<td class="xmpcode">
2640	<pre>F = set([A'P+PA PB;B'P zeros(size(B,2))]+M < 0);
2641	F = set(kyp(A,B,P,M) < 0);</pre>
2642	</td>
2643	</tr>
2644	</table>
2645	<p>The dedicated solver <a href="solvers.htm#kypd">KYPD</a> can only
2646	be used if the variable <b>P</b> is symmetric matrix, obtained directly
2647	from <font color="#0000ff"><a href="reference.htm#sdpvar">sdpvar</a></font>,
2648	used only in 1 constraint.  This means that you cannot use
2649	<a href="solvers.htm#kypd">KYPD</a> if you want to impose explicit
2650	constraints (including positive definiteness) on <b>P</b>. However,
2651	positive definiteness of <b>P </b>is in some cases implied by the
2652	KYP constraint</p>
2653	</td>
2654	</tr>
2655	<tr>
2656	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2657	Related commands</th>
2658	</tr>
2659	<tr>
2660	<td class="tabxpl"><font color="#0000ff">
2661	<a href="reference.htm#sdpvar">sdpvar</a>,
2662	<a href="reference.htm#set">set</a></font></td>
2663	</tr>
2664	</table>
2665	</td>
2666	</tr>
2667	</table>
2668	<p> </p>
2669	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
2670	<tr>
2671	<td class="tableheader">
2672	<p class="tableheader"><a name="linearize">LINEARIZE</a></p>
2673	</td>
2674	</tr>
2675	<tr>
2676	<td>
2677	<table cellspacing="0" cellpadding="4" width="100%" border="0">
2678	<tr>
2679	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2680	Syntax</th>
2681	<td class="code" valign="top" nowrap width="100%"><code>h = linearize(p)</code></td>
2682	</tr>
2683	<tr>
2684	<td class="tabxpl">
2685	<table border="0">
2686	<tr>
2687	<td>
2688	<p align="right"><font face="Courier New" size="2">h:</font></p>
2689	</td>
2690	<td>sdpvar object </td>
2691	</tr>
2692	<tr>
2693	<td>
2694	<p align="right"><font face="Courier New" size="2">p:</font></p>
2695	</td>
2696	<td>sdpvar object</td>
2697	</tr>
2698	</table>
2699	</td>
2700	</tr>
2701	<tr>
2702	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2703	Description</th>
2704	</tr>
2705	<tr>
2706	<td class="tabxpl">Returns linearization p(double(x)) + dp(double(x))*(x-double(x))
2707	where x is the <a href="reference.htm#sdpvar">sdpvar</a> variables
2708	defining the polynomial p(x).</td>
2709	</tr>
2710	<tr>
2711	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2712	Examples</th>
2713	</tr>
2714	<tr>
2715	<td class="tabxpl">The linearization is performed at the current value
2716	of <a href="reference.htm#double">double</a>(x)<table cellpadding="10" width="100%">
2717	<tr>
2718	<td class="xmpcode">
2719	<pre>x = sdpvar(1,1);
2720	f = x^2;
2721	assign(x,1);
2722	sdisplay(linearize(f))
2723	<font color="#000000">ans = </font></pre>
2724	<pre><font color="#000000"> '-1+2x'</font>
2725
2726	assign(x,3);
2727	sdisplay(linearize(f))
2728	<font color="#000000">ans = </font></pre>
2729	<pre><font color="#000000"> '-9+6x'</font></pre>
2730	</td>
2731	</tr>
2732	</table>
2733	<p>The command of-course applies to matrices as well </p>
2734	<table cellpadding="10" width="100%">
2735	<tr>
2736	<td class="xmpcode">
2737	<pre>p11 = sdpvar(1,1);p12 = sdpvar(1,1);p22 = sdpvar(1,1);
2738	P = [p11 p12;p12 p22];
2739	assign(P,[3 2;2 5])</pre>
2740	<pre>sdisplay(linearize(P*P))<font color="#000000">
2741	ans = </font></pre>
2742	<pre><font color="#000000"> '-13+6p11+4p12'   '-16+2p11+8p12+2p22'
2743	'-16+2p11+8p12+2p22' '-29+4p12+10p22' </font> </pre>
2744	</td>
2745	</tr>
2746	</table>
2747	</td>
2748	</tr>
2749	<tr>
2750	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2751	Related commands</th>
2752	</tr>
2753	<tr>
2754	<td class="tabxpl"><a href="reference.htm#jacobian">jacobian</a>,
2755	<a href="reference.htm#hessian">hessian</a>,
2756	<a href="reference.htm#sdisplay">sdisplay</a>,
2757	<a href="reference.htm#sdpvar">sdpvar</a></td>
2758	</tr>
2759	</table>
2760	</td>
2761	</tr>
2762	</table>
2763	<p> </p>
2764	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
2765	<tr>
2766	<td class="tableheader">
2767	<p class="tableheader"><a name="logdet">LOGDET</a></p>
2768	</td>
2769	</tr>
2770	<tr>
2771	<td>
2772	<table cellspacing="0" cellpadding="4" width="100%" border="0">
2773	<tr>
2774	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2775	Syntax</th>
2776	<td class="code" valign="top" nowrap width="100%"><code>p = logdet(x)</code></td>
2777	</tr>
2778	<tr>
2779	<td class="tabxpl">
2780	<table border="0">
2781	<tr>
2782	<td>
2783	<p align="right"><font face="Courier New" size="2">p:</font></p>
2784	</td>
2785	<td>sdpvar object (only useful in
2786	<a href="reference.htm#logdet">solvesdp</a>)</td>
2787	</tr>
2788	<tr>
2789	<td>
2790	<p align="right"><font face="Courier New" size="2">x:</font></p>
2791	</td>
2792	<td>sdpvar object</td>
2793	</tr>
2794	</table>
2795	</td>
2796	</tr>
2797	<tr>
2798	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2799	Description</th>
2800	</tr>
2801	<tr>
2802	<td class="tabxpl">logdet is used to define objective functions in
2803	MAXDET problems. This command will likely become obsolete in a
2804	future version.</td>
2805	</tr>
2806	<tr>
2807	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2808	Examples</th>
2809	</tr>
2810	<tr>
2811	<td class="tabxpl">See <a href="ellipsoidal.htm">MAXDET example</a>.</td>
2812	</tr>
2813	<tr>
2814	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2815	Related commands</th>
2816	</tr>
2817	<tr>
2818	<td class="tabxpl"><a href="reference.htm#solvesdp">solvesdp</a>,
2819	<a href="reference.htm#sdpvar">sdpvar</a></td>
2820	</tr>
2821	</table>
2822	</td>
2823	</tr>
2824	</table>
2825	<p> </p>
2826	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
2827	<tr>
2828	<td class="tableheader">
2829	<p class="tableheader"><a name="lowrank">LOWRANK</a></p>
2830	</td>
2831	</tr>
2832	<tr>
2833	<td>
2834	<table cellspacing="0" cellpadding="4" width="100%" border="0">
2835	<tr>
2836	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2837	Syntax</th>
2838	<td class="code" valign="top" nowrap width="100%"><code>H = lowrank(F,x)</code></td>
2839	</tr>
2840	<tr>
2841	<td class="tabxpl">
2842	<table border="0">
2843	<tr>
2844	<td>
2845	<p align="right"><font face="Courier New">H</font><font face="Courier New" size="2">:</font></p>
2846	</td>
2847	<td>set object (only useful in
2848	<a href="reference.htm#logdet">solvesdp</a>)</td>
2849	</tr>
2850	<tr>
2851	<td>
2852	<p align="right"><font face="Courier New" size="2">F:</font></p>
2853	</td>
2854	<td>sdpvar object</td>
2855	</tr>
2856	<tr>
2857	<td>
2858	<font face="Courier New">x:</font></td>
2859	<td>sdpvar object</td>
2860	</tr>
2861	</table>
2862	</td>
2863	</tr>
2864	<tr>
2865	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2866	Description</th>
2867	</tr>
2868	<tr>
2869	<td class="tabxpl">lowrank is used to declare that a semidefinite
2870	constraint uses <b>data</b> with low rank.</td>
2871	</tr>
2872	<tr>
2873	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2874	Examples</th>
2875	</tr>
2876	<tr>
2877	<td class="tabxpl"><p>Define a semidefinite constraint
2878	with low-rank data matrices (both variables in <b>x</b> enter the
2879	constraint via rank-2 matrices)</p>
2880	<table cellpadding="10" width="100%">
2881	<tr>
2882	<td class="xmpcode">
2883	<pre>x = sdpvar(2,1);
2884	C = randn(10,10);C = C*C';
2885	R = randn(10,2);
2886	F = set(C-Rdiag(x)R' > 0);</pre>
2887	</td>
2888	</tr>
2889	</table>
2890	<p>If a low-rank data exploiting solver is available (currently
2891	only<a target="_blank" href="http://dollar.biz.uiowa.edu/~burer/software/SDPLR/">
2892	SDPLR</a>), we can ask YALMIP to extract low-rank
2893	information and pass this to the solver. </p>
2894	<table cellpadding="10" width="100%">
2895	<tr>
2896	<td class="xmpcode">
2897	<pre>solvesdp(F + lowrank(F),-sum(x),sdpsettings('solver','sdplr'));</pre>
2898	</td>
2899	</tr>
2900	</table>
2901	<p>In some cases, the low-rank structure is only with respect to
2902	some variables, as here where <b>y</b> enters via a full rank matrix.
2903	In this cases, it might be counter productive to try to exploit
2904	the (non-existing) low rank.</p>
2905	<table cellpadding="10" width="100%">
2906	<tr>
2907	<td class="xmpcode">
2908	<pre>x = sdpvar(2,1);
2909	y = sdpvar(1,1);
2910	C = randn(10,10);C = C*C';
2911	R = randn(10,2);
2912	S = randn(10,10);S = S+S';
2913	F = set(C-Rdiag(x)R'-y*S > 0);</pre>
2914	</td>
2915	</tr>
2916	</table>
2917	<p>In this case, it is possible to tell YALMIP which variables
2918	enter in a low-rank fashion, here <b>x</b>.<p>
2919	</p><table cellpadding="10" width="100%">
2920	<tr>
2921	<td class="xmpcode">
2922	<pre>solvesdp(F+lowrank(F,x),-sum(x)-y,sdpsettings('solver','sdplr'));</pre>
2923	</td>
2924	</tr>
2925	</table>
2926	<p>An alternative way to work with low rank data matrices is to
2927	use the option sdpsettings('sdprl.maxrank'). By changing this
2928	setting from it default value of 0, YALMIP will automatically
2929	check all data matrices for low rank structure, and send low rank
2930	data to the solver if the rank is less than the value of
2931	sdpsettings('sdprl.maxrank'). Hence, YALMIP will exploit low rank
2932	w.r.t <b>x</b> but not <b>y</b> in the following solution. </p>
2933	<table cellpadding="10" width="100%">
2934	<tr>
2935	<td class="xmpcode">
2936	<pre>solvesdp(F,-sum(x)-y,sdpsettings('solver','sdplr','sdplr.maxrank',2));</pre>
2937	</td>
2938	</tr>
2939	</table>
2940	</td>
2941	</tr>
2942	<tr>
2943	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2944	Related commandss</th>
2945	</tr>
2946	<tr>
2947	<td class="tabxpl"><a href="reference.htm#solvesdp">solvesdp</a></td>
2948	</tr>
2949	</table>
2950	</td>
2951	</tr>
2952	</table>
2953	<p> </p>
2954	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table10">
2955	<tr>
2956	<td class="tableheader">
2957	<p class="tableheader"><a name="monolist">MONOLIST</a></p>
2958	</td>
2959	</tr>
2960	<tr>
2961	<td>
2962	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table11">
2963	<tr>
2964	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2965	Syntax </th>
2966	<td class="code" valign="top" nowrap width="100%"><code>v =
2967	monolist(x,d)</code></td>
2968	</tr>
2969	<tr>
2970	<td class="tabxpl">
2971	<table border="0" id="table12">
2972	<tr>
2973	<td>
2974	<p align="right"><font face="Courier New">x</font><font face="Courier New" size="2">:</font></p>
2975	</td>
2976	<td>sdpvar object </td>
2977	</tr>
2978	<tr>
2979	<td>
2980	<p align="right"><font face="Courier New">d</font><font face="Courier New" size="2">:</font></p>
2981	</td>
2982	<td>Maximum degrees</td>
2983	</tr>
2984	</table>
2985	</td>
2986	</tr>
2987	<tr>
2988	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2989	Description</th>
2990	</tr>
2991	<tr>
2992	<td class="tabxpl">monolist is used to generate monomials</td>
2993	</tr>
2994	<tr>
2995	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
2996	Examples</th>
2997	</tr>
2998	<tr>
2999	<td class="tabxpl">Create all monomials of degree less than 2<table cellpadding="10" width="100%" id="table13">
3000	<tr>
3001	<td class="xmpcode">
3002	<pre>sdpvar x y
3003	v = monolist([x y],2);
3004	sdisplay(v')
3005
3006	<font color="#000000">ans = </font></pre>
3007	<pre><font color="#000000"> '1' 'x' 'y' 'x^2' 'xy' 'y^2'</font></pre>
3008	</td>
3009	</tr>
3010	</table>
3011	<p>The command support different degrees on different variables<br>
3012	</p><table cellpadding="10" width="100%" id="table14">
3013	<tr>
3014	<td class="xmpcode">
3015	<pre>sdpvar x y
3016	v = monolist([x y],[2 3]);
3017	sdisplay(v')
3018
3019	<font color="#000000">ans = </font></pre>
3020	<pre><font color="#000000"> '1' 'x' 'y' 'x^2' 'xy' 'y^2' 'x^2y' 'xy^2' 'y^3'</font></pre>
3021	</td>
3022	</tr>
3023	</table>
3024	</td>
3025	</tr>
3026	<tr>
3027	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3028	Related commands</th>
3029	</tr>
3030	<tr>
3031	<td class="tabxpl"><a href="reference.htm#sdisplay">sdisplay</a>,
3032	<a href="reference.htm#sdpvar">sdpvar</a></td>
3033	</tr>
3034	</table>
3035	</td>
3036	</tr>
3037	</table>
3038	<p> </p>
3039	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
3040	<tr>
3041	<td class="tableheader">
3042	<p class="tableheader"><a name="plot">PLOT</font></a></p>
3043	</td>
3044	</tr>
3045	<tr>
3046	<td>
3047	<table cellspacing="0" cellpadding="4" width="100%" border="0">
3048	<tr>
3049	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3050	Syntax<p></p>
3051	</th>
3052	<td class="code" valign="top" nowrap width="100%"><code>p = plot(F,x,c,n,options)</code></td>
3053	</tr>
3054	<tr>
3055	<td class="tabxpl">
3056	<table border="0">
3057	<tr>
3058	<td>
3059	<p align="right"><font face="Courier New" size="2">F:</font></p>
3060	</td>
3061	<td>set object</td>
3062	</tr>
3063	<tr>
3064	<td>
3065	<p align="right"><font face="Courier New">x</font><font face="Courier New" size="2">:</font></p>
3066	</td>
3067	<td>sdpvar variable</td>
3068	</tr>
3069	<tr>
3070	<td>
3071	<p align="right"><font face="Courier New" size="2">c:</font></p>
3072	</td>
3073	<td>char or double</td>
3074	</tr>
3075	<tr>
3076	<td>
3077	<p align="right"><font face="Courier New">n</font><font face="Courier New" size="2">:</font></p>
3078	</td>
3079	<td>double</td>
3080	</tr>
3081	<tr>
3082	<td><font face="Courier New">options:</font></td>
3083	<td>options structure from <a href="#sdpsettings">sdpsettings</a></td>
3084	</tr>
3085	</table>
3086	</td>
3087	</tr>
3088	<tr>
3089	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3090	Description</th>
3091	</tr>
3092	<tr>
3093	<td class="tabxpl">plot is used to plot the (projection) of the feasible
3094	set</td>
3095	</tr>
3096	<tr>
3097	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3098	Examples</th>
3099	</tr>
3100	<tr>
3101	<td class="tabxpl">Define a set in <b>R<sup>3</sup></b><table cellpadding="10" width="100%">
3102	<tr>
3103	<td class="xmpcode">
3104	<pre>x = sdpvar(3,1);
3105
3106	F = set([1 x(2);x(2) x(1)])+set(3 > x);
3107	F = F + set([1 x';x eye(3)]>0) + set(sum(x)>x'*x);</pre>
3108	</td>
3109	</tr>
3110	</table>
3111	<p>Plot the feasible set, projected on <b>(x<sub>1</sub>,x<sub>3</sub>)</b></p>
3112	<table cellpadding="10" width="100%">
3113	<tr>
3114	<td class="xmpcode">
3115	<pre>plot(F,[x(1);x(3)])</pre>
3116	</td>
3117	</tr>
3118	</table>
3119	<p>By default, the feasible set is projected to <b>R<sup>3</sup></b>
3120	(the three variables with lowest index in YALMIP) </p>
3121	<table cellpadding="10" width="100%">
3122	<tr>
3123	<td class="xmpcode">
3124	<pre>plot(F)</pre>
3125	</td>
3126	</tr>
3127	</table>
3128	<p>Why not the feasible set on <b>x<sub>1</sub>=0.5</b></p>
3129	<table cellpadding="10" width="100%">
3130	<tr>
3131	<td class="xmpcode">
3132	<pre>plot(replace(F,x(1),0.5))</pre>
3133	</td>
3134	</tr>
3135	</table>
3136	<p>A third argument can be used to control the color </p>
3137	<table cellpadding="10" width="100%">
3138	<tr>
3139	<td class="xmpcode">
3140	<pre>plot(F,[],'b')</pre>
3141	</td>
3142	</tr>
3143	</table>
3144	<p>A fourth argument can be used to control the accuracy</p>
3145	<table cellpadding="10" width="100%">
3146	<tr>
3147	<td class="xmpcode">
3148	<pre>plot(F,[],[],150)</pre>
3149	</td>
3150	</tr>
3151	</table>
3152	<p>The fifth argument can be used to pass an options structure for
3153	the solver</p>
3154	<table cellpadding="10" width="100%">
3155	<tr>
3156	<td class="xmpcode">
3157	<pre>plot(F,[],[],[],sdpsettings('solver','sedumi','verbose',0));</pre>
3158	</td>
3159	</tr>
3160	</table>
3161	<p>To avoid strange looking plots, you should ensure that your
3162	feasible set is bounded. One way to that is to add bounds on on
3163	variables.</p>
3164	<table cellpadding="10" width="100%" id="table86">
3165	<tr>
3166	<td class="xmpcode">
3167	<pre>plot(F+set(-100 < recover(depends(F)) < 100));</pre>
3168	</td>
3169	</tr>
3170	</table>
3171	<p>Note that plotting the feasible set requires solving the
3172	associated optimization problem repeatedly. Hence, for feasible
3173	sets defined by a lot of constraints and variables, it may take a
3174	long time to generate the figure (controlled by the accuracy level
3175	in the fourth argument, 25 points is default for 2D and 100 for 3D
3176	figures, although much more is recommended for smooth figures). For small problems, a large portion of
3177	the solution time can easily be dominated by overhead costs.
3178	Hence, it is recommended to use a solver with low overhead (for
3179	SDP problems, <a href="solvers.htm#pensdp">PENSDP</a> is
3180	recommended)<p>Also note that when you plot sets with constraints involving
3181	<a href="extoperators.htm">nonlinear
3182	operators</a> and polynomials, it is recommended that you specify the variables
3183	of interest in the second argument (YALMIP may otherwise plot the set
3184	with respect to auxiliary variables introduced during the construction
3185	of the conic model.)</td>
3186	</tr>
3187	<tr>
3188	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3189	Related commands</th>
3190	</tr>
3191	<tr>
3192	<td class="tabxpl"><a href="reference.htm#set">set</a>,<a href="#plotsdpvar"> plot</a></td>
3193	</tr>
3194	</table>
3195	</td>
3196	</tr>
3197	</table>
3198	<p> </p>
3199	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table88">
3200	<tr>
3201	<td class="tableheader">
3202	<p class="tableheader"><a name="plotsdpvar">PLOT</font></a></p>
3203	</td>
3204	</tr>
3205	<tr>
3206	<td>
3207	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table89">
3208	<tr>
3209	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3210	Syntax<p></p>
3211	</th>
3212	<td class="code" valign="top" nowrap width="100%"><code>plot(t)</code></td>
3213	</tr>
3214	<tr>
3215	<td class="tabxpl">
3216	<table border="0" id="table90">
3217	<tr>
3218	<td>
3219	<p align="right"><font face="Courier New">t</font><font face="Courier New" size="2">:</font></p>
3220	</td>
3221	<td>sdpvar object</td>
3222	</tr>
3223	</table>
3224	</td>
3225	</tr>
3226	<tr>
3227	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3228	Description</th>
3229	</tr>
3230	<tr>
3231	<td class="tabxpl">plot is used to plot the PWA model of a
3232	variable generated using <a href="extoperators.htm">nonlinear
3233	operators</a> that can be modeled with linear constraints</td>
3234	</tr>
3235	<tr>
3236	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3237	Examples</th>
3238	</tr>
3239	<tr>
3240	<td class="tabxpl">Plot the L<sub>1</sub> norm<table cellpadding="10" width="100%" id="table91">
3241	<tr>
3242	<td class="xmpcode">
3243	<pre>x = sdpvar(2,1);
3244	clf;plot(norm(x,1))</pre>
3245	</td>
3246	</tr>
3247	</table>
3248	<p>Or a more complex PWA expression</p>
3249	<table cellpadding="10" width="100%" id="table99">
3250	<tr>
3251	<td class="xmpcode">
3252	<pre>x = sdpvar(2,1);
3253	clf;plot(norm(randn(5,2)x,1)+ max(x)-5x(2))</pre>
3254	</td>
3255	</tr>
3256	</table>
3257	<p>Notice that the command by default plots the function over a
3258	grid from -100 to 100. This can currently not be changed.
3259	However, we can easily circumvent this by using the main
3260	function used in plot. </p>
3261	<table cellpadding="10" width="100%" id="table92">
3262	<tr>
3263	<td class="xmpcode">
3264	<pre>p = pwa(norm(randn(5,2)x,1)+ max(x)-5x(2),set(-1<x<1));
3265	clf;plot(p)</pre>
3266	</td>
3267	</tr>
3268	</table>
3269	</td>
3270	</tr>
3271	<tr>
3272	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3273	Related commands</th>
3274	</tr>
3275	<tr>
3276	<td class="tabxpl"><a href="reference.htm#plot">plot</a> </td>
3277	</tr>
3278	</table>
3279	</td>
3280	</tr>
3281	</table>
3282	<p> </p>
3283	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
3284	<tr>
3285	<td class="tableheader">
3286	<p class="tableheader"><a name="polyprint">POLYPRINT</a></p>
3287	</td>
3288	</tr>
3289	<tr>
3290	<td>
3291	<table cellspacing="0" cellpadding="4" width="100%" border="0">
3292	<tr>
3293	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3294	Description</th>
3295	</tr>
3296	<tr>
3297	<td class="tabxpl">Polyprint is obsolete and replaced with
3298	<a href="reference.htm#sdisplay">sdisplay</a></td>
3299	</tr>
3300	</table>
3301	</td>
3302	</tr>
3303	</table>
3304	<p> </p>
3305	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table1">
3306	<tr>
3307	<td class="tableheader">
3308	<p class="tableheader"><a name="primalize">PRIMALIZE</a></p>
3309	</td>
3310	</tr>
3311	<tr>
3312	<td>
3313	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table2">
3314	<tr>
3315	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3316	Syntax</th>
3317	<td class="code" valign="top" nowrap width="100%"><code>
3318	[Fp,objp,y] = primalize(F,obj)</code></td>
3319	</tr>
3320	<tr>
3321	<td class="tabxpl">
3322	<table border="0" id="table3">
3323	<tr>
3324	<td>
3325	<p align="right"><font face="Courier New" size="2">F:</font></p>
3326	</td>
3327	<td>set object in dual SDP form</td>
3328	</tr>
3329	<tr>
3330	<td>
3331	<p align="right"><font face="Courier New" size="2">obj:</font></p>
3332	</td>
3333	<td>sdpvar object (primal cost)</td>
3334	</tr>
3335	<tr>
3336	<td>
3337	<p align="right"><font face="Courier New" size="2">Fp:</font></p>
3338	</td>
3339	<td>set object in primal SDP form</td>
3340	</tr>
3341	<tr>
3342	<td>
3343	<p align="right"><font face="Courier New">objd</font><font face="Courier New" size="2">:</font></p>
3344	</td>
3345	<td>sdpvar object (primal cost)</td>
3346	</tr>
3347	<tr>
3348	<td>
3349	<p align="right"><font face="Courier New">y</font><font face="Courier New" size="2">:</font></p>
3350	</td>
3351	<td>sdpvar object (detected dual variables)</td>
3352	</tr>
3353	</table>
3354	</td>
3355	</tr>
3356	<tr>
3357	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3358	Description</th>
3359	</tr>
3360	<tr>
3361	<td class="tabxpl">dualize is used to convert a SDP problem given
3362	in primal form to the corresponding dual problem.</td>
3363	</tr>
3364	<tr>
3365	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3366	Examples</th>
3367	</tr>
3368	<tr>
3369	<td class="tabxpl">See <a href="dual.htm">examples</a>.</td>
3370	</tr>
3371	<tr>
3372	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3373	Related commands</th>
3374	</tr>
3375	<tr>
3376	<td class="tabxpl">
3377	<a href="reference.htm#dualize">dualize</a></td>
3378	</tr>
3379	</table>
3380	</td>
3381	</tr>
3382	</table>
3383	<p> </p>
3384	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table81">
3385	<tr>
3386	<td class="tableheader">
3387	<p class="tableheader"><a name="pwf">PWF</a></p>
3388	</td>
3389	</tr>
3390	<tr>
3391	<td>
3392	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table82">
3393	<tr>
3394	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3395	Syntax</th>
3396	<td class="code" valign="top" nowrap width="100%"><code>t = double(f1,F1,f2,F2,...,fn,Fn)</code></td>
3397	</tr>
3398	<tr>
3399	<td class="tabxpl">
3400	<table border="0" id="table83">
3401	<tr>
3402	<td>
3403	<p align="right"><font face="Courier New">t</font><font face="Courier New" size="2">:</font></p>
3404	</td>
3405	<td>sdpvar object</td>
3406	</tr>
3407	<tr>
3408	<td>
3409	<p align="right"><font face="Courier New" size="2">fi:</font></p>
3410	</td>
3411	<td>sdpvar object (function value)</td>
3412	</tr>
3413	<tr>
3414	<td>
3415	<font face="Courier New">F</font><font face="Courier New" size="2">i</font></td>
3416	<td>set object (region guard)</td>
3417	</tr>
3418	<tr>
3419	<td>
3420	</td>
3421	<td> </td>
3422	</tr>
3423	</table>
3424	</td>
3425	</tr>
3426	<tr>
3427	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3428	Description</th>
3429	</tr>
3430	<tr>
3431	<td class="tabxpl">pwf is used to define piece-wise functions.</td>
3432	</tr>
3433	<tr>
3434	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3435	Examples</th>
3436	</tr>
3437	<tr>
3438	<td class="tabxpl">Consider a model where the function has the
3439	value <b>f1(x)</b> when the constraint <b>F1(x)</b> holds and <b>
3440	f2(x)</b> when the constraint <b>F2(x)</b> holds. This can be
3441	modeled as<table cellpadding="10" width="100%" id="table84">
3442	<tr>
3443	<td class="xmpcode">
3444	<pre>sdpvar x y
3445	F1 = set(x+y<0);
3446	F2 = set(x+y>0);
3447	f1 = (x+3)^2+(y+2)^2+7;
3448	f2 = (x+3)^2+(y-2)^2+9;
3449	t = pwf(f1,F1,f2,F2);</pre>
3450	</td>
3451	</tr>
3452	</table>
3453	<p>The variable returned from the function is a so called
3454	<a href="extoperators.htm">nonlinear operator</a>. To minimize
3455	the piece-wise function, we use the variable <b>t</b> as usual and
3456	simply call <a href="reference.htm#solvesdp">solvesdp</a>. YALMIP
3457	will automatically try to construct a model that can be
3458	solved. In this case, YALMIP will derive a mixed integer second
3459	order cone problem. </p>
3460	<table cellpadding="10" width="100%" id="table85">
3461	<tr>
3462	<td class="xmpcode">
3463	<pre>solvesdp([],t);</pre>
3464	</td>
3465	</tr>
3466	</table>
3467	<p>Support for piece-wise functions is still limited, but can
3468	easily be improved if wanted. At the moment, the function can be
3469	defined using arbitrary functions and sets, but when it comes down to
3470	computing things, only convex quadratic functions and regions
3471	defined by convex quadratic constraints are allowed.</td>
3472	</tr>
3473	<tr>
3474	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3475	Related commands</th>
3476	</tr>
3477	<tr>
3478	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>,
3479	<a href="reference.htm#solvesdp">solvesdp</a></td>
3480	</tr>
3481	</table>
3482	</td>
3483	</tr>
3484	</table>
3485	<p> </p>
3486	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table15">
3487	<tr>
3488	<td class="tableheader">
3489	<p class="tableheader"><a name="rank">RANK</a></p>
3490	</td>
3491	</tr>
3492	<tr>
3493	<td>
3494	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table16">
3495	<tr>
3496	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3497	Syntax</th>
3498	<td class="code" valign="top" nowrap width="100%"><code>r = rank(x)</code></td>
3499	</tr>
3500	<tr>
3501	<td class="tabxpl">
3502	<table border="0" id="table17">
3503	<tr>
3504	<td>
3505	<p align="right"><font face="Courier New">r</font><font face="Courier New" size="2">:</font></p>
3506	</td>
3507	<td>sdpvar object (only useful in set object)</td>
3508	</tr>
3509	<tr>
3510	<td>
3511	<p align="right"><font face="Courier New">x</font><font face="Courier New" size="2">:</font></p>
3512	</td>
3513	<td>sdpvar object</td>
3514	</tr>
3515	</table>
3516	</td>
3517	</tr>
3518	<tr>
3519	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3520	Description</th>
3521	</tr>
3522	<tr>
3523	<td class="tabxpl">rank is mainly used for creating rank
3524	constraints.</td>
3525	</tr>
3526	<tr>
3527	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3528	Examples</th>
3529	</tr>
3530	<tr>
3531	<td class="tabxpl">The <a href="extoperators.htm">nonlinear
3532	operator</a> rank is used to add rank constraints to SDP
3533	problems. <table cellpadding="10" width="100%" id="table18">
3534	<tr>
3535	<td class="xmpcode">
3536	<pre>F = F + set(rank(X)<=1)</pre>
3537	</td>
3538	</tr>
3539	</table>
3540	<p>For more information, please study the <a href="ranksdp.htm">
3541	rank constrained</a> example.</td>
3542	</tr>
3543	<tr>
3544	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3545	Related commands</th>
3546	</tr>
3547	<tr>
3548	<td class="tabxpl"><a href="#set">set</a></td>
3549	</tr>
3550	</table>
3551	</td>
3552	</tr>
3553	</table>
3554	<p> </p>
3555	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
3556	<tr>
3557	<td class="tableheader">
3558	<p class="tableheader"><a name="rcone">RCONE</a></p>
3559	</td>
3560	</tr>
3561	<tr>
3562	<td>
3563	<table cellspacing="0" cellpadding="4" width="100%" border="0">
3564	<tr>
3565	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3566	Syntax<p> </p>
3567	</th>
3568	<td class="code" valign="top" nowrap width="100%"><code>c = rcone(x,y,z)</code></td>
3569	</tr>
3570	<tr>
3571	<td class="tabxpl">
3572	<table border="0">
3573	<tr>
3574	<td>
3575	<p align="right"><font face="Courier New" size="2">c:</font></p>
3576	</td>
3577	<td>sdpvar object (only useful in set object)</td>
3578	</tr>
3579	<tr>
3580	<td>
3581	<p align="right"><font face="Courier New" size="2">x:</font></p>
3582	</td>
3583	<td>sdpvar object (vector)</td>
3584	</tr>
3585	<tr>
3586	<td>
3587	<p align="right"><font face="Courier New" size="2">y:</font></p>
3588	</td>
3589	<td>sdpvar object (scalar)</td>
3590	</tr>
3591	<tr>
3592	<td>
3593	<p align="right"><font face="Courier New" size="2">z:</font></p>
3594	</td>
3595	<td>sdpvar object (scalar)</td>
3596	</tr>
3597	</table>
3598	</td>
3599	</tr>
3600	<tr>
3601	<th class="doc" valign="top" align="left" bgcolor="#eeeeee" rowspan="2">
3602	Description</th>
3603	</tr>
3604	<tr>
3605	<td class="tabxpl">rcone is used to define the constraints <b>z<sup>T</sup>z<2xy</b>,
3606	<b>x</b>,<b>y>0</b> (The rotated Lorentz cone)</td>
3607	</tr>
3608	<tr>
3609	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3610	Examples</th>
3611	</tr>
3612	<tr>
3613	<td class="tabxpl">Constraining the squared Euclidean norm of a vector
3614	to be less than 2 is done with<table cellpadding="10" width="100%">
3615	<tr>
3616	<td class="xmpcode">
3617	<pre>x = sdpvar(n,1);
3618	F = set(rcone(x,1,1));</pre>
3619	</td>
3620	</tr>
3621	</table>
3622	</td>
3623	</tr>
3624	<tr>
3625	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3626	Related commands</th>
3627	</tr>
3628	<tr>
3629	<td class="tabxpl"><a href="reference.htm#cone">cone</a>,
3630	<a href="reference.htm#set">set</a>,
3631	<a href="reference.htm#sdpvar">sdpvar</a></td>
3632	</tr>
3633	</table>
3634	</td>
3635	</tr>
3636	</table>
3637	<p> </p>
3638	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
3639	<tr>
3640	<td class="tableheader">
3641	<p class="tableheader"><a name="saveampl">SAVEAMPL</a></p>
3642	</td>
3643	</tr>
3644	<tr>
3645	<td>
3646	<table cellspacing="0" cellpadding="4" width="100%" border="0">
3647	<tr>
3648	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3649	Syntax<p> </p>
3650	</th>
3651	<td class="code" valign="top" nowrap width="100%"><code>saveampl(F,h,filename)</code></td>
3652	</tr>
3653	<tr>
3654	<td class="tabxpl">
3655	<table border="0">
3656	<tr>
3657	<td>
3658	<p align="right"><font face="Courier New" size="2">F:</font></p>
3659	</td>
3660	<td>set object describing the constraints</td>
3661	</tr>
3662	<tr>
3663	<td>
3664	<p align="right"><font face="Courier New">h</font><font face="Courier New" size="2">:</font></p>
3665	</td>
3666	<td>sdpvar object describing the objective function</td>
3667	</tr>
3668	<tr>
3669	<td>
3670	<p align="right"><font face="Courier New">filename</font><font face="Courier New" size="2">:</font></p>
3671	</td>
3672	<td>char (can be [])</td>
3673	</tr>
3674	</table>
3675	</td>
3676	</tr>
3677	<tr>
3678	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3679	Description</th>
3680	</tr>
3681	<tr>
3682	<td class="tabxpl">saveampl exports a YALMIP model to an AMPL model.</td>
3683	</tr>
3684	<tr>
3685	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3686	Examples</th>
3687	</tr>
3688	<tr>
3689	<td class="tabxpl">Well, not much to say. Here is a simple MILP exported
3690	to an AMPL model<table cellpadding="10" width="100%">
3691	<tr>
3692	<td class="xmpcode">
3693	<pre>x = sdpvar(3,1);
3694	A = randn(5,3);
3695	b = randn(5,1);
3696	c = randn(3,1);
3697	F = set(A*x < b) + set(integer(x(2:3)));
3698	saveampl(F,c'*x,'myamplmodel.mod');</pre>
3699	</td>
3700	</tr>
3701	</table>
3702	</td>
3703	</tr>
3704	<tr>
3705	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3706	Related commands</th>
3707	</tr>
3708	<tr>
3709	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>,
3710	<a href="reference.htm#solvesdp">solvesdp</a></td>
3711	</tr>
3712	</table>
3713	</td>
3714	</tr>
3715	</table>
3716	<p> </p>
3717	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table26">
3718	<tr>
3719	<td class="tableheader">
3720	<p class="tableheader"><a name="savesdpafile">SAVESDPAFILE</a></p>
3721	</td>
3722	</tr>
3723	<tr>
3724	<td>
3725	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table27">
3726	<tr>
3727	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3728	Syntax<p> </p>
3729	</th>
3730	<td class="code" valign="top" nowrap width="100%"><code>savesdpafile(F,h,filename)</code></td>
3731	</tr>
3732	<tr>
3733	<td class="tabxpl">
3734	<table border="0" id="table28">
3735	<tr>
3736	<td>
3737	<p align="right"><font face="Courier New" size="2">F:</font></p>
3738	</td>
3739	<td>set object describing the constraints</td>
3740	</tr>
3741	<tr>
3742	<td>
3743	<p align="right"><font face="Courier New">h</font><font face="Courier New" size="2">:</font></p>
3744	</td>
3745	<td>sdpvar object describing the objective function</td>
3746	</tr>
3747	<tr>
3748	<td>
3749	<p align="right"><font face="Courier New">filename</font><font face="Courier New" size="2">:</font></p>
3750	</td>
3751	<td>char (can be [])</td>
3752	</tr>
3753	</table>
3754	</td>
3755	</tr>
3756	<tr>
3757	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3758	Description</th>
3759	</tr>
3760	<tr>
3761	<td class="tabxpl">savesdpafile exports a YALMIP model to an SDPA
3762	ASCII format</td>
3763	</tr>
3764	<tr>
3765	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3766	Examples</th>
3767	</tr>
3768	<tr>
3769	<td class="tabxpl">Export SDP problem to ASCII file.<table cellpadding="10" width="100%" id="table29">
3770	<tr>
3771	<td class="xmpcode">
3772	<pre>A = randn(3,3);A = -A*A';
3773	P = sdpvar(3,3);
3774	F = set(P>0) + set(A'P+PA < -eye(3));
3775	saveampl(F,trace(P),'mysdpamodel');</pre>
3776	</td>
3777	</tr>
3778	</table>
3779	</td>
3780	</tr>
3781	<tr>
3782	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3783	Related commands</th>
3784	</tr>
3785	<tr>
3786	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>,
3787	<a href="reference.htm#solvesdp">solvesdp</a></td>
3788	</tr>
3789	</table>
3790	</td>
3791	</tr>
3792	</table>
3793	<p> </p>
3794	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
3795	<tr>
3796	<td class="tableheader">
3797	<p class="tableheader"><a name="sdisplay">SDISPLAY</a></p>
3798	</td>
3799	</tr>
3800	<tr>
3801	<td>
3802	<table cellspacing="0" cellpadding="4" width="100%" border="0">
3803	<tr>
3804	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3805	Syntax</th>
3806	<td class="code" valign="top" nowrap width="100%"><code>t =
3807	sdisplay(p)</code></td>
3808	</tr>
3809	<tr>
3810	<td class="tabxpl">
3811	<table border="0">
3812	<tr>
3813	<td>
3814	<p align="right"><font face="Courier New" size="2">t:</font></p>
3815	</td>
3816	<td>cell array of chars</td>
3817	</tr>
3818	<tr>
3819	<td>
3820	<p align="right"><font face="Courier New" size="2">p:</font></p>
3821	</td>
3822	<td>sdpvar object</td>
3823	</tr>
3824	</table>
3825	</td>
3826	</tr>
3827	<tr>
3828	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3829	Description</th>
3830	</tr>
3831	<tr>
3832	<td class="tabxpl">Tries to display an sdpvar object in symbolic
3833	MATLAB
3834	form</td>
3835	</tr>
3836	<tr>
3837	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3838	Examples</th>
3839	</tr>
3840	<tr>
3841	<td class="tabxpl">The command is useful for displaying polynomial
3842	<a href="reference.htm#sdpvar">sdpvar</a> objects<table cellpadding="10" width="100%">
3843	<tr>
3844	<td class="xmpcode">
3845	<pre>x = sdpvar(1,1);y = sdpvar(1,1);
3846	f = [x;x^2+y+x*y];
3847	sdisplay(f)
3848
3849	<font color="#000000">ans = </font></pre>
3850	<pre><font color="#000000"> 'x'
3851	'y+x^2+xy'</font></pre>
3852	</td>
3853	</tr>
3854	</table>
3855	<p>The command tries to find the symbolic names of variables, but
3856	if this fails, the variable name <b>internal</b> will be used.
3857	Additionally, variables defined using nonlinear operators can
3858	currently not be displayed.</p>
3859	</td>
3860	</tr>
3861	<tr>
3862	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3863	Related commands</th>
3864	</tr>
3865	<tr>
3866	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>,
3867	<a href="reference.htm#jacobian">jacobian</a>,
3868	<a href="reference.htm#hessian">hessian</a></td>
3869	</tr>
3870	</table>
3871	</td>
3872	</tr>
3873	</table>
3874	<p> </p>
3875	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
3876	<tr>
3877	<td class="tableheader">
3878	<p class="tableheader"><a name="sdpsettings">SDPSETTINGS</font></a></p>
3879	</td>
3880	</tr>
3881	<tr>
3882	<td>
3883	<table cellspacing="0" cellpadding="4" width="100%" border="0">
3884	<tr>
3885	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3886	Syntax<p> </p>
3887	</th>
3888	<td class="code" valign="top" nowrap width="100%"><code>options =
3889	sdpsettings('field',value,'field','value',...)</code></td>
3890	</tr>
3891	<tr>
3892	<td class="tabxpl">
3893	<table border="0">
3894	<tr>
3895	<td>
3896	<p align="right"><font face="Courier New" size="2">'field':</font></p>
3897	</td>
3898	<td>Option to be modified</td>
3899	</tr>
3900	<tr>
3901	<td>
3902	<p align="right"><font face="Courier New" size="2">'value':</font></p>
3903	</td>
3904	<td>New setting</td>
3905	</tr>
3906	</table>
3907	</td>
3908	</tr>
3909	<tr>
3910	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3911	Description</th>
3912	</tr>
3913	<tr>
3914	<td class="tabxpl">sdpsettings is used to set parameters to control
3915	the behavior of solvers and YALMIP</td>
3916	</tr>
3917	<tr>
3918	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
3919	Examples</th>
3920	</tr>
3921	<tr>
3922	<td class="tabxpl">The easiest way to see what the possible options
3923	are is to define a options structure and display it<table cellpadding="10" width="100%">
3924	<tr>
3925	<td class="xmpcode">
3926	<pre>ops = sdpsettings</pre>
3927	<pre><font color="#000000">ops = </font></pre>
3928	<pre><font color="#000000"> solver: ''
3929	verbose: 1
3930	warning: 1
3931	cachesolvers: 0
3932	beeponproblem: [-5 -4 -3 -2 -1]
3933	showprogress: 0
3934	saveduals: 1
3935	removeequalities: 0
3936	savesolveroutput: 0
3937	savesolverinput: 0
3938	convertconvexquad: 1
3939	radius: Inf
3940	relax: 0
3941	usex0: 0
3942	shift: 0
3943	savedebug: 0
3944	sos: [1x1 struct]
3945	moment: [1x1 struct]
3946	bnb: [1x1 struct]
3947	bpmpd: [1x1 struct]
3948	bmibnb: [1x1 struct]
3949	cutsdp: [1x1 struct]
3950	global: [1x1 struct]
3951	cdd: [1x1 struct]
3952	clp: [1x1 struct]
3953	cplex: [1x1 struct]
3954	csdp: [1x1 struct]
3955	dsdp: [1x1 struct]
3956	glpk: [1x1 struct]
3957	kypd: [1x1 struct]
3958	lmilab: [1x1 struct]
3959	lmirank: [1x1 struct]
3960	lpsolve: [1x1 struct]
3961	maxdet: [1x1 struct]
3962	nag: [1x1 struct]
3963	penbmi: [1x1 struct]
3964	pennlp: [1x1 struct]
3965	pensdp: [1x1 struct]
3966	sdpa: [1x1 struct]
3967	sdplr: [1x1 struct]
3968	sdpt3: [1x1 struct]
3969	sedumi: [1x1 struct]
3970	qsopt: [1x1 struct]
3971	xpress: [1x1 struct]
3972	quadprog: [1x1 struct]
3973	linprog: [1x1 struct]
3974	bintprog: [1x1 struct]
3975	fmincon: [1x1 struct]
3976	fminsearch: [1x1 struct]</font></pre>
3977	</td>
3978	</tr>
3979	</table>
3980	<p>Changing a value from the default settings is done as</p>
3981	<table cellpadding="10" width="100%">
3982	<tr>
3983	<td class="xmpcode">
3984	<pre>ops = sdpsettings('solver','dsdp','verbose',0)</pre>
3985	</td>
3986	</tr>
3987	</table>
3988	<p><b><a name="sdpsettings_solver"></a>solver</b></p>
3989	<p>In the code above, we told YALMIP to use the solver DSDP, and to
3990	run in silent mode. The possible values to give to the field <code>
3991	solver </code>can be found in the <a href="solvers.htm">introduction
3992	to the solvers</a>. If the solver DSDP not is found, an error
3993	message will be reported. To let YALMIP select the solver, use
3994	the solver tag <code>''</code>. If you give a comma-separated list of solvers
3995	such as <code>'dsdp,csdp,sdpa'</code>, YALMIP will select based
3996	on this preference. If you add a wildcard in the end <code>'dsdp,csdp,sdpa,*'</code>,
3997	YALMIP will select another solver if none of the solvers in the
3998	list were found. </p>
3999	<p><b>verbose</b></p>
4000	<p>By setting <code>verbose</code> to 0, the solvers will run with
4001	minimal display. By increasing the value, the display level is controlled
4002	(typically 1 gives modest display level while 2 gives an awful amount
4003	of information printed). </p>
4004	<p><b>warning</b></p>
4005	<p>The <code>warning</code> option can be used
4006	to get a warning displayed when a solver has run into some kind of
4007	problem (recommended to be used if the solver is run in silent mode).
4008	</p>
4009	<p><b>beeponproblem</b></p>
4010	<p>The field <code>beeponproblem</code> contains a list of error codes
4011	(see yalmiperror). YALMIP will beep if any of these errors occurs
4012	(nice feature if you're taking a coffee break during heavy calculations).</p>
4013	<p><b>showprogress</b></p>
4014	<p>When the field <code>showprogress</code> is set to 1, the user
4015	can see what YALMIP currently is doing (might be a good idea for large-scale
4016	problems). </p>
4017	<p><b>cachesolvers</b></p>
4018	<p>Everytime <a href="#solvesdp">solvesdp</a> is called, YALMIP checks
4019	for available solvers. This can take a while on some systems (some
4020	networks), so it is possible to avoid doing this check every call.
4021	Set <code>cachesolvers</code> to 1, and YALMIP will remember the solvers
4022	(using a persistent variable) found in the first call to
4023	<a href="#solvesdp">solvesdp</a>. If solvers are added to the path
4024	after the first call, YALMIP will not detect this. Hence, after adding
4025	a solver to the path the work-space must be cleared or
4026	<a href="#solvesdp">solvesdp</a> must be called once with <code>cachesolvers</code>
4027	set to 0.</p>
4028	<p><b>removeequalities</b></p>
4029	<p>When the field <code>removeequalities</code> is set to 1, YALMIP
4030	removes equality constraints using a QR decomposition and reformulates
4031	the problem using a smaller set of variables. If <code>removeequalities</code> is set to
4032	2, YALMIP
4033	removes equality constraints using a basis derived directly from
4034	independent columns of the equality constraints (higher
4035	possibility of maintaining sparsity than the QR approach, but
4036	may lead to a numerically poor basis). With <code>removeequalities</code>
4037	set to -1, equalities are removed by YALMIP by converting them to
4038	double-sided inequalities. When set to 0, YALMIP does nothing if
4039	the solver supports equalities. If the solver does not support
4040	equalities, YALMIP uses double-sided inequalities.</p>
4041	<p><b>saveduals</b></p>
4042	<p>If the field <code>saveduals</code> is set to 0, the dual variables
4043	will not be saved in YALMIP. This might be useful for large sparse
4044	problems with a dense dual variable. Setting the field to 0 will then
4045	save some memory.</p>
4046	<p><b>savesolverinput, savesolveroutput</b></p>
4047	<p>The fields <code>savesolverinput</code> and <code>savesolveroutput</code>
4048	can be used to see what is actually sent to and returned from the
4049	solver. This data will then be available in the output structure from
4050	solvesdp.</p>
4051	<p><b>convertconvexquad</b></p>
4052	<p>With <code>convertconvexquad</code> set to 1, YALMIP will try to
4053	convert quadratic constraints to second order cones.</p>
4054	<p>A constraint <b><font face="Tahoma">\|\|x\|\|≤radius</font><font face="Times New Roman">
4055	</font></b>on the vector of all involved decision variables can be
4056	added by changing the field <code>radius</code> to a finite positive
4057	value. This can improve numerical performance in some cases. In fact,
4058	the field <code>radius</code> may be an <a href="#sdpvar">sdpvar</a>
4059	object. If you work with semidefinite programs and standard convex
4060	programming, it is recommended to keep the feature on. However,
4061	if you work with more general nonlinear optimization problem, it
4062	is most often recommended to turn the conversion off.</p>
4063	<p><b>shift</b></p>
4064	<p>Strict inequalities can be modeled in YALMIP by using the > and
4065	< when defining constraints. The behaviour of this feature can be
4066	altered using the option <code>shift</code>. For constraints
4067	defined
4068	with strict constraints, a small perturbation is added (semidefinite
4069	constraints <b><font face="Tahoma">F(x)>0</font></b> are changed to
4070	<b><font face="Tahoma">F(x)≥shift*I</font></b>, while element-wise
4071	constraints are changed from <b><font face="Tahoma">F(x)>0 </font>
4072	</b>to <b><font face="Tahoma">F(x)≥shift</font></b>). Note that the
4073	use of this feature does not guarantee a strictly feasible solution.
4074	This depends on the solver.</p>
4075	<p><b>relax</b></p>
4076	<p>If <code>relax</code> is set to 1, all nonlinearities and integrality
4077	constraints will be disregarded. Integer variables are relaxed to
4078	continuous variables and nonlinear variables are treated as independent
4079	variables (i.e., <b>x</b> and <b>x</b><sup><b>2</b></sup> will be
4080	treated as two separate variables).</p>
4081	<p><b>usex0</b></p>
4082	<p>The current solution (the value returned from the
4083	<a href="#double">double</a> command) can be used as an initial guess
4084	when solving an optimization problem. Setting the field <code>usex0</code>
4085	to 1 tells YALMIP to supply the current values as an initial guess
4086	to the solver.</p>
4087	<p><b>solver options</b></p>
4088	<p>The options structure also contains a number of structures with
4089	parameters used in the specific solver. As an example, the following
4090	parameters can be tuned for SeDuMi (for details, the user is referred
4091	to the manual of the specific solver).</p>
4092	<table cellpadding="10" width="100%">
4093	<tr>
4094	<td class="xmpcode">
4095	<pre>ops.sedumi
4096	<font color="#000000">ans =
4097	alg: 2
4098	theta: 0.2500
4099	beta: 0.5000
4100	eps: 1.0000e-009
4101	bigeps: 0.0010
4102	numtol: 1.0000e-005
4103	denq: 0.7500
4104	denf: 10
4105	vplot: 0
4106	maxiter: 100
4107	stepdif: 1
4108	w: [1 1]
4109	stopat: -1
4110	cg: [1x1 struct]
4111	chol: [1x1 struct]</font></pre>
4112	</td>
4113	</tr>
4114	</table>
4115	<p>Finally, a convenient way to alter a lot of options is to send
4116	an existing options structure as the first input argument.</p>
4117	<table cellpadding="10" width="100%">
4118	<tr>
4119	<td class="xmpcode">
4120	<pre>ops = sdpsettings('solver','sdpa');
4121	ops = sdpsettings(ops,'verbose',0);</pre>
4122	</td>
4123	</tr>
4124	</table>
4125	</td>
4126	</tr>
4127	<tr>
4128	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4129	Related commands</th>
4130	</tr>
4131	<tr>
4132	<td class="tabxpl"><a href="reference.htm#solvesdp">solvesdp</a></td>
4133	</tr>
4134	</table>
4135	</td>
4136	</tr>
4137	</table>
4138	<p> </p>
4139	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
4140	<tr>
4141	<td class="tableheader">
4142	<p class="tableheader"><a name="sdpvar">SDPVAR</font></a></p>
4143	</td>
4144	</tr>
4145	<tr>
4146	<td>
4147	<table cellspacing="0" cellpadding="4" width="100%" border="0">
4148	<tr>
4149	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4150	Syntax<p> </p>
4151	</th>
4152	<td class="code" valign="top" nowrap width="100%"><code>x = sdpvar(n,m,'field','type')</code></td>
4153	</tr>
4154	<tr>
4155	<td class="tabxpl">
4156	<table border="0">
4157	<tr>
4158	<td>
4159	<p align="right"><font face="Courier New" size="2">n:</font></p>
4160	</td>
4161	<td>Height(s)</td>
4162	</tr>
4163	<tr>
4164	<td>
4165	<p align="right"><font face="Courier New" size="2">m:</font></p>
4166	</td>
4167	<td>Width(s)</td>
4168	</tr>
4169	<tr>
4170	<td>
4171	<p align="right"><font face="Courier New" size="2">'field':</font></p>
4172	</td>
4173	<td>char {'real','complex'}</td>
4174	</tr>
4175	<tr>
4176	<td>
4177	<p align="right"><font face="Courier New" size="2">'type':</font></p>
4178	</td>
4179	<td>char {'symmetric','full','hermitian','toeplitz','hankel','skew'}</td>
4180	</tr>
4181	</table>
4182	</td>
4183	</tr>
4184	<tr>
4185	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4186	Description</th>
4187	</tr>
4188	<tr>
4189	<td class="tabxpl">sdpvar is used to define symbolic decision variables.</td>
4190	</tr>
4191	<tr>
4192	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4193	Examples</th>
4194	</tr>
4195	<tr>
4196	<td class="tabxpl">A scalar real-valued variable is defined with<table cellpadding="10" width="100%">
4197	<tr>
4198	<td class="xmpcode">
4199	<pre>P = sdpvar(1,1)</pre>
4200	</td>
4201	</tr>
4202	</table>
4203	<p>A square real-valued symmetric matrix is obtained with </p>
4204	<table cellpadding="10" width="100%">
4205	<tr>
4206	<td class="xmpcode">
4207	<pre>P = sdpvar(n,n)</pre>
4208	</td>
4209	</tr>
4210	</table>
4211	<p>The commands above can be simplified by only giving one argument
4212	when defining a symmetric matrix or a scalar (this might not work
4213	on MATLAB 5.3 and earlier version). </p>
4214	<table cellpadding="10" width="100%">
4215	<tr>
4216	<td class="xmpcode">
4217	<pre>P = sdpvar(n)</pre>
4218	</td>
4219	</tr>
4220	</table>
4221	<p>We can also define the same matrix using a more verbose notation.
4222	</p>
4223	<table cellpadding="10" width="100%">
4224	<tr>
4225	<td class="xmpcode">
4226	<pre>P = sdpvar(n,n,'symmetric')</pre>
4227	</td>
4228	</tr>
4229	</table>
4230	<p>A fully parameterized square matrix requires a third argument.</p>
4231	<table cellpadding="10" width="100%">
4232	<tr>
4233	<td class="xmpcode">
4234	<pre>P = sdpvar(n,n,'full')</pre>
4235	</td>
4236	</tr>
4237	</table>
4238	<p>A square complex-valued fully parameterized matrix is obtained
4239	with </p>
4240	<table cellpadding="10" width="100%">
4241	<tr>
4242	<td class="xmpcode">
4243	<pre>P = sdpvar(n,n,'full','complex')</pre>
4244	</td>
4245	</tr>
4246	</table>
4247	<p>YALMIP tries to complete the third and fourth argument, so an equivalent
4248	command is </p>
4249	<table cellpadding="10" width="100%">
4250	<tr>
4251	<td class="xmpcode">
4252	<pre>P = sdpvar(n,n,'sy','co')</pre>
4253	</td>
4254	</tr>
4255	</table>
4256	<p>Variables can alternatively be defined using command
4257	line syntax.</p>
4258	<table cellpadding="10" width="100%">
4259	<tr>
4260	<td class="xmpcode">
4261	<pre>sdpvar x y z(1,1) u(2,2) v(2,3,'full','complex')</pre>
4262	</td>
4263	</tr>
4264	</table>
4265	<p>A lot of users seem to get stuck initially on simple things
4266	such as defining a diagonal matrix. The most important thing to
4267	remember when working with YALMIP is that almost all MATLAB
4268	operators can be applied also on sdpvar objects. Hence, we
4269	create diagonal matrices with </p>
4270	<table cellpadding="10" width="100%" id="table104">
4271	<tr>
4272	<td class="xmpcode">
4273	<pre>X = diag(sdpvar(n,1));</pre>
4274	</td>
4275	</tr>
4276	</table>
4277	<p>Or Hankel...</p>
4278	<table cellpadding="10" width="100%" id="table105">
4279	<tr>
4280	<td class="xmpcode">
4281	<pre>X = hankel(sdpvar(n,1));</pre>
4282	</td>
4283	</tr>
4284	</table>
4285	<p>A typical situation is that several identical variables are
4286	needed, and the most straightforward way to code this is to use
4287	a loop.</p>
4288	<table cellpadding="10" width="100%" id="table67">
4289	<tr>
4290	<td class="xmpcode">
4291	<pre>for i = 1:100; X{i} = sdpvar(5,5);end</pre>
4292	</td>
4293	</tr>
4294	</table>
4295	<p>However, a much more efficient way to implement this is to use
4296	vector valued dimensions (this currently only works if all
4297	matrices are symmetric or full)</p>
4298	<table cellpadding="10" width="100%" id="table68">
4299	<tr>
4300	<td class="xmpcode">
4301	<pre>X = sdpvar(5ones(1,100),5ones(1,100));</pre>
4302	</td>
4303	</tr>
4304	</table>
4305	<p>Another way to create multi-dimensional matrices is to use more
4306	than 2 dimension arguments</p>
4307	<table cellpadding="10" width="100%" id="table141">
4308	<tr>
4309	<td class="xmpcode">
4310	<pre>X = sdpvar(5,5,100);</pre>
4311	</td>
4312	</tr>
4313	</table>
4314	<p>The benefit with this approach is that this variable can be
4315	manipulated as standard 1D and 2D sdpvar objects.</td>
4316	</tr>
4317	<tr>
4318	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4319	Related commands</th>
4320	</tr>
4321	<tr>
4322	<td class="tabxpl"><a href="reference.htm#assign">assign</a>,
4323	<a href="reference.htm#binvar">binvar</a>,
4324	<a href="reference.htm#intvar">intvar</a>,
4325	<a href="reference.htm#set">set</a></td>
4326	</tr>
4327	</table>
4328	</td>
4329	</tr>
4330	</table>
4331	<p> </p>
4332	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
4333	<tr>
4334	<td class="tableheader">
4335	<p class="tableheader"><a name="see">SEE</a></p>
4336	</td>
4337	</tr>
4338	<tr>
4339	<td>
4340	<table cellspacing="0" cellpadding="4" width="100%" border="0">
4341	<tr>
4342	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4343	Syntax</th>
4344	<td class="code" valign="top" nowrap width="100%"><code>see(x)</code></td>
4345	</tr>
4346	<tr>
4347	<td class="tabxpl">
4348	<table border="0">
4349	<tr>
4350	<td><font face="Courier New" size="2">x:</font></td>
4351	<td>sdpvar object</td>
4352	</tr>
4353	</table>
4354	</td>
4355	</tr>
4356	<tr>
4357	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4358	Description</th>
4359	</tr>
4360	<tr>
4361	<td class="tabxpl">see is used to print the base matrices of an
4362	<a href="#sdpvar">sdpvar</a> object.</td>
4363	</tr>
4364	<tr>
4365	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4366	Examples</th>
4367	</tr>
4368	<tr>
4369	<td class="tabxpl">A symmetric 2x2 matrix has the following base matrices<table cellpadding="10" width="100%">
4370	<tr>
4371	<td class="xmpcode">
4372	<pre>x = sdpvar(2,2);
4373	see(x)
4374	<font color="#000000">
4375	Constant matrix
4376
4377	0 0
4378	0 0</font></pre>
4379	<pre><font color="#000000">Base matrices
4380
4381	1 0
4382	0 0</font></pre>
4383	<pre><font color="#000000">
4384	0 1
4385	1 0</font></pre>
4386	<pre><font color="#000000">
4387	0 0
4388	0 1</font></pre>
4389	<pre><font color="#000000">
4390	Used variables
4391
4392	1 2 3</font></pre>
4393	</td>
4394	</tr>
4395	</table>
4396	<p>When an <a href="reference.htm#sdpvar">sdpvar</a> object is altered,
4397	the base matrices change </p>
4398	<table cellpadding="10" width="100%">
4399	<tr>
4400	<td class="xmpcode">
4401	<pre> </pre>
4402	<pre>x = sdpvar(1,1);
4403	see(2*x-3)
4404	Constant matrix
4405
4406	<font color="#000000"> -3</font></pre>
4407	<pre><font color="#000000">Base matrices
4408
4409	2</font></pre>
4410	<pre><font color="#000000">
4411	Used variables
4412
4413	4</font></pre>
4414	<pre> </pre>
4415	</td>
4416	</tr>
4417	</table>
4418	</td>
4419	</tr>
4420	<tr>
4421	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4422	Related commands</th>
4423	</tr>
4424	<tr>
4425	<td class="tabxpl"><a href="reference.htm#getbase">getbase</a>,
4426	<a href="reference.htm#getbasematrix">getbasematrix</a>,
4427	<a href="reference.htm#getvariables">getvariables</a>,
4428	<a href="reference.htm#recover">recover</a>,
4429	<a href="reference.htm#sdpvar">sdpvar</a></td>
4430	</tr>
4431	</table>
4432	</td>
4433	</tr>
4434	</table>
4435	<p> </p>
4436	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
4437	<tr>
4438	<td class="tableheader">
4439	<p class="tableheader"><a name="set">SET</a></p>
4440	</td>
4441	</tr>
4442	<tr>
4443	<td>
4444	<table cellspacing="0" cellpadding="4" width="100%" border="0">
4445	<tr>
4446	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4447	Syntax<p> </p>
4448	</th>
4449	<td class="code" valign="top" nowrap width="100%"><code>F = set(X,'tag')</code></td>
4450	</tr>
4451	<tr>
4452	<td class="tabxpl">
4453	<table border="0">
4454	<tr>
4455	<td>
4456	<p align="right"><font face="Courier New" size="2">F:</font></p>
4457	</td>
4458	<td>set object</td>
4459	</tr>
4460	<tr>
4461	<td>
4462	<p align="right"><font face="Courier New" size="2">X:</font></p>
4463	</td>
4464	<td>sdpvar or constraint object, or string</td>
4465	</tr>
4466	<tr>
4467	<td>
4468	<p align="right"><font face="Courier New" size="2">'tag':</font></p>
4469	</td>
4470	<td>char</td>
4471	</tr>
4472	</table>
4473	</td>
4474	</tr>
4475	<tr>
4476	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4477	Description</th>
4478	</tr>
4479	<tr>
4480	<td class="tabxpl">set is used to define the constraints in a problem</td>
4481	</tr>
4482	<tr>
4483	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4484	Example</th>
4485	</tr>
4486	<tr>
4487	<td class="tabxpl">To begin with, note that it is possible to create
4488	an empty <a href="reference.htm#lmi">set</a> object (this can be useful
4489	in some loop-constructs).<table cellpadding="10" width="100%">
4490	<tr>
4491	<td class="xmpcode">
4492	<pre>F = set([]);</pre>
4493	</td>
4494	</tr>
4495	</table>
4496	<p>Secondly, do not confuse the <a href="reference.htm#lmi">set</a>
4497	object with the standard command set in MATLAB. Yes, it is confusing,
4498	but set was the only relevant short word for defining the feasible
4499	set that I could come up with...</p>
4500	<p>Constraining a scalar variable to be larger than 5 is done with
4501	</p>
4502	<table cellpadding="10" width="100%">
4503	<tr>
4504	<td class="xmpcode">
4505	<pre>x = sdpvar(1,1)
4506	F = set(x > 5)</pre>
4507	</td>
4508	</tr>
4509	</table>
4510	<p>The variable <code>F</code> serves as a container for all constraints
4511	here. Defining a matrix to be both positive definite and elementwise
4512	positive is done with </p>
4513	<table cellpadding="10" width="100%">
4514	<tr>
4515	<td class="xmpcode">
4516	<pre>P = sdpvar(n,n);
4517	F = set(P > 0) + set(P(:) > 0);</pre>
4518	</td>
4519	</tr>
4520	</table>
4521	<p>A string-notation can also be used </p>
4522	<table cellpadding="10" width="100%">
4523	<tr>
4524	<td class="xmpcode">
4525	<pre>F = set('P > 0') + set('P(:) > 0')</pre>
4526	</td>
4527	</tr>
4528	</table>
4529	<p>A <a href="reference.htm#set">set</a> object can be tagged with
4530	a description (which can be useful for referencing a particular constraint
4531	in, e.g., <a href="reference.htm#dual">dual</a>) </p>
4532	<table cellpadding="10" width="100%">
4533	<tr>
4534	<td class="xmpcode">
4535	<pre>F = set(P > 0,'positive definite');
4536	F = F + set(P(:)>0,'positive elements')</pre>
4537	</td>
4538	</tr>
4539	</table>
4540	<p>Second order cone constraints <b><font face="Tahoma">\|\|Ax+b\|\|<c<sup>T</sup>x+d</font></b>
4541	can be added with the function <a href="reference.htm#cone">cone</a>
4542	</p>
4543	<table cellpadding="10" width="100%">
4544	<tr>
4545	<td class="xmpcode">
4546	<pre>F = set(cone(Ax+b,c'x+d))</pre>
4547	</td>
4548	</tr>
4549	</table>
4550	<p>Equality constraints can also be defined. A constraint that the
4551	sum of the vector components is equal to 1 is obtained with </p>
4552	<table cellpadding="10" width="100%">
4553	<tr>
4554	<td class="xmpcode">
4555	<pre>F = set(sum(x) == 1)</pre>
4556	</td>
4557	</tr>
4558	</table>
4559	<p>In general, it should be remembered that YALMIP uses MATLAB standard
4560	when it comes to comparison of matrices and scalars. Hence, the following
4561	code will constrain all diagonal elements to be larger than 1. </p>
4562	<table cellpadding="10" width="100%">
4563	<tr>
4564	<td class="xmpcode">
4565	<pre>F = set(diag(P) > 1))</pre>
4566	</td>
4567	</tr>
4568	</table>
4569	<p>Double-sided constraints and extensions can easily be defined.</p>
4570	<table cellpadding="10" width="100%">
4571	<tr>
4572	<td class="xmpcode">
4573	<pre>F = set(2 > diag(P) > 1 > sum(sum(P)))</pre>
4574	</td>
4575	</tr>
4576	</table>
4577	<p>It is possible to have complex and integer valued constraints.
4578	No special code is necessary. To create a complex-valued integer Hermitian
4579	matrix and constrain it to be positive definite, we write </p>
4580	<table cellpadding="10" width="100%">
4581	<tr>
4582	<td class="xmpcode">
4583	<pre>P = intvar(3,3,'hermitian','complex');
4584	F = set(P > 0)</pre>
4585	</td>
4586	</tr>
4587	</table>
4588	<p>Notice that <a href="reference.htm#lmi">set</a> objects
4589	can be referenced </p>
4590	<table cellpadding="10" width="100%">
4591	<tr>
4592	<td class="xmpcode">
4593	<pre>F = set(P > 0) + set(A'P+PA < 0) + set(P(1,1) > 0)+set(P(1,:) > 0);
4594	F_lmi = F(1:2)
4595	F_element = F(find(is(F,'element-wise')))</pre>
4596	</td>
4597	</tr>
4598	</table>
4599	<p>Finally, note that YALMIP does essentially not distinguish
4600	between strict and non-strict inequalities. Hence, the following
4601	two constraints are in almost all cases the same.</p>
4602	<table cellpadding="10" width="100%" id="table123">
4603	<tr>
4604	<td class="xmpcode">
4605	<pre>F = set(P > 0) + set(trace(P) < 1);
4606	G = set(P >= 0) + set(trace(P) <= 1);</pre>
4607	</td>
4608	</tr>
4609	</table>
4610	<p>Please read the <a href="#reallystrict">FAQ</a> for more
4611	information on the difference.</td>
4612	</tr>
4613	<tr>
4614	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4615	Related commands</th>
4616	</tr>
4617	<tr>
4618	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>,
4619	<a href="reference.htm#integer">integer</a>,
4620	<a href="reference.htm#binary">binary</a>,
4621	<a href="reference.htm#solvesdp">solvesdp</a></td>
4622	</tr>
4623	</table>
4624	</td>
4625	</tr>
4626	</table>
4627	<p> </p>
4628	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
4629	<tr>
4630	<td class="tableheader">
4631	<p class="tableheader"><a name="setsdpvar">SETSDPVAR</font></a></p>
4632	</td>
4633	</tr>
4634	<tr>
4635	<td>
4636	<table cellspacing="0" cellpadding="4" width="100%" border="0">
4637	<tr>
4638	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4639	Syntax</th>
4640	<td class="code" valign="top" nowrap width="100%"><code>assign(X,Y)</code></td>
4641	</tr>
4642	<tr>
4643	<td class="tabxpl">
4644	<table border="0">
4645	<tr>
4646	<td>
4647	<p align="right"><font face="Courier New" size="2">X:</font></p>
4648	</td>
4649	<td>sdpvar object</td>
4650	</tr>
4651	<tr>
4652	<td>
4653	<p align="right"><font face="Courier New" size="2">Y:</font></p>
4654	</td>
4655	<td>double</td>
4656	</tr>
4657	</table>
4658	</td>
4659	</tr>
4660	<tr>
4661	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4662	Description</th>
4663	</tr>
4664	<tr>
4665	<td class="tabxpl">setsdpvar is obsolete. Use <a href="reference.htm#assign">assign</a>
4666	instead.</td>
4667	</tr>
4668	<tr>
4669	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4670	Related commands</th>
4671	</tr>
4672	<tr>
4673	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>, <a href="reference.htm#assign">assign</a></td>
4674	</tr>
4675	</table>
4676	</td>
4677	</tr>
4678	</table>
4679	<p> </p>
4680	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
4681	<tr>
4682	<td class="tableheader">
4683	<p class="tableheader"><a name="solvemp">SOLVEMP</font></a></p>
4684	</td>
4685	</tr>
4686	<tr>
4687	<td>
4688	<table cellspacing="0" cellpadding="4" width="100%" border="0">
4689	<tr>
4690	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4691	Syntax<p> </p>
4692	</th>
4693	<td class="code" valign="top" nowrap width="100%"><code>[mpsolution,diagnostic]
4694	= solvemp(F,h,ops,x)</code></td>
4695	</tr>
4696	<tr>
4697	<td class="tabxpl">
4698	<table border="0">
4699	<tr>
4700	<td>
4701	<p align="right"><font face="Courier New" size="2">mpsolution:</font></p>
4702	</td>
4703	<td>Multiparametric solution</td>
4704	</tr>
4705	<tr>
4706	<td>
4707	<p align="right"><font face="Courier New" size="2">diagnostic:</font></p>
4708	</td>
4709	<td>Output structure</td>
4710	</tr>
4711	<tr>
4712	<td>
4713	<p align="right"><font face="Courier New" size="2">F:</font></p>
4714	</td>
4715	<td>set object describing the constraints. Can be [].</td>
4716	</tr>
4717	<tr>
4718	<td>
4719	<p align="right"><font face="Courier New" size="2">h:</font></p>
4720	</td>
4721	<td>sdpvar-object describing the objective function. Can be [].</td>
4722	</tr>
4723	<tr>
4724	<td>
4725	<p align="right"><font face="Courier New" size="2">ops:</font></p>
4726	</td>
4727	<td>options structure from sdpsettings. Can be [].</td>
4728	</tr>
4729	<tr>
4730	<td>
4731	<p align="right"><font face="Courier New">x</font><font face="Courier New" size="2">:</font></p>
4732	</td>
4733	<td>parametric variables.</td>
4734	</tr>
4735	</table>
4736	</td>
4737	</tr>
4738	<tr>
4739	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4740	Description</th>
4741	</tr>
4742	<tr>
4743	<td class="tabxpl">solvemp is used for solving multiparametric problems.</td>
4744	</tr>
4745	<tr>
4746	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4747	Examples</th>
4748	</tr>
4749	<tr>
4750	<td class="tabxpl">solvemp is used in the same way as
4751	<a href="#solvesdp">solvesdp</a>, the only difference being the fourth
4752	additional argument to define the parametric variables. See the
4753	<a href="mp.htm">multiparametric example</a> for details.</td>
4754	</tr>
4755	<tr>
4756	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4757	Related commands</th>
4758	</tr>
4759	<tr>
4760	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>,
4761	<a href="reference.htm#set">set</a>,
4762	<a href="reference.htm#sdpsettings">sdpsettings</a>,
4763	<a href="reference.htm#solvemoment">solvemoment</a>,
4764	<a href="#solvesdp">solvesdp</a>, <a href="reference.htm#solvesos">
4765	solvesos</a></td>
4766	</tr>
4767	</table>
4768	</td>
4769	</tr>
4770	</table>
4771	<p> </p>
4772	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
4773	<tr>
4774	<td class="tableheader">
4775	<p class="tableheader"><a name="solvemoment">SOLVEMOMENT</font></a></p>
4776	</td>
4777	</tr>
4778	<tr>
4779	<td>
4780	<table cellspacing="0" cellpadding="4" width="100%" border="0">
4781	<tr>
4782	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4783	Syntax<p> </p>
4784	</th>
4785	<td class="code" valign="top" nowrap width="100%"><code>[sol,xoptimal,momentdata,sos] = solvemoment(F,h,options,d)</code></td>
4786	</tr>
4787	<tr>
4788	<td class="tabxpl">
4789	<table border="0">
4790	<tr>
4791	<td>
4792	<p align="right"><font face="Courier New" size="2">sol:</font></p>
4793	</td>
4794	<td>diagnostics structure from solvesdp</td>
4795	</tr>
4796	<tr>
4797	<td>
4798	<p align="right"><font face="Courier New" size="2">F:</font></p>
4799	</td>
4800	<td>set object describing the constraints</td>
4801	</tr>
4802	<tr>
4803	<td>
4804	<p align="right"><font face="Courier New">xoptimal</font><font face="Courier New" size="2">:</font></p>
4805	</td>
4806	<td>Extracted global solutions</td>
4807	</tr>
4808	<tr>
4809	<td>
4810	<p align="right"><font face="Courier New">momentdata</font><font face="Courier New" size="2">:</font></p>
4811	</td>
4812	<td>Moment matrices etc.</td>
4813	</tr>
4814	<tr>
4815	<td>
4816	<p align="right"><font face="Courier New">sos</font><font face="Courier New" size="2">:</font></p>
4817	</td>
4818	<td>Associated sum-of-squares decompositions</td>
4819	</tr>
4820	<tr>
4821	<td>
4822	<p align="right"><font face="Courier New" size="2">h:</font></p>
4823	</td>
4824	<td>sdpvar object describing objective</td>
4825	</tr>
4826	<tr>
4827	<td>
4828	<p align="right"><font face="Courier New" size="2">options:</font></p>
4829	</td>
4830	<td>structure from sdpsettings</td>
4831	</tr>
4832	<tr>
4833	<td>
4834	<p align="right"><font face="Courier New" size="2">d:</font></p>
4835	</td>
4836	<td>integer>0</td>
4837	</tr>
4838	</table>
4839	</td>
4840	</tr>
4841	<tr>
4842	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4843	Description</th>
4844	</tr>
4845	<tr>
4846	<td class="tabxpl">solvemoment computes lower bounds to polynomial
4847	programs using Lasserre's moment-method.</td>
4848	</tr>
4849	<tr>
4850	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4851	Examples</th>
4852	</tr>
4853	<tr>
4854	<td class="tabxpl">The command is used for finding lower bounds on
4855	a polynomial h(x), subject to constraints F(x), where F(x) is a collection
4856	of polynomial inequalities. The following example is taken from [?].<table cellpadding="10" width="100%">
4857	<tr>
4858	<td class="xmpcode">
4859	<pre>x1 = sdpvar(1,1);x2 = sdpvar(1,1);x3 = sdpvar(1,1);
4860	h = -2*x1+x2-x3;
4861	F = set(x1(4x1-4x2+4x3-20)+x2(2x2-2x3+9)+x3(2*x3-13)+24>0)
4862	F = F + set(4-(x1+x2+x3)>0);
4863	F = F + set(6-(3*x2+x3)>0);
4864	F = F + set(2-x1>0);
4865	F = F + set(3-x3>0);
4866	F = F + set(x1>0);
4867	F = F + set(x2>0);
4868	F = F + set(x3>0);
4869	solvemoment(F,h);
4870	<font color="#000000">double(h)
4871	ans =</font></pre>
4872	<pre><font color="#000000"> -6.0000</font></pre>
4873	</td>
4874	</tr>
4875	</table>
4876	<p>In the code above, we solved the problem with the lowest possible
4877	lifting (decided by YALMIP), and the lower bound turned out to be
4878	-6. A higher order relaxation gives better bounds. </p>
4879	<table cellpadding="10" width="100%">
4880	<tr>
4881	<td class="xmpcode">
4882	<pre>solvemoment(F,h,[],2);
4883	double(h)
4884	<font color="#000000">ans =</font></pre>
4885	<pre><font color="#000000"> -5.69</font>
4886	</pre>
4887	<pre>solvemoment(F,h,[],3);
4888	double(h)
4889	<font color="#000000">ans =</font></pre>
4890	<pre><font color="#000000"> -4.0685</font>
4891	</pre>
4892	<pre>solvemoment(F,h,[],4);
4893	double(h)
4894	<font color="#000000">ans =</font></pre>
4895	<pre><font color="#000000"> -4.0000</font></pre>
4896	<pre> </pre>
4897	<pre> </pre>
4898	</td>
4899	</tr>
4900	</table>
4901	<p>For a more complete introduction, please study the extensive
4902	<a href="moment.htm">examples</a>.</td>
4903	</tr>
4904	<tr>
4905	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4906	Related commands</th>
4907	</tr>
4908	<tr>
4909	<td class="tabxpl"><a href="reference.htm#solvesdp">solvesdp</a>,
4910	<a href="reference.htm#solvesos">solvesos</a>,
4911	<a href="reference.htm#sdpvar">sdpvar</a>,
4912	<a href="reference.htm#set">set</a></td>
4913	</tr>
4914	</table>
4915	</td>
4916	</tr>
4917	</table>
4918	<p> </p>
4919	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
4920	<tr>
4921	<td class="tableheader">
4922	<p class="tableheader"><a name="solvesdp">SOLVESDP</font></a></p>
4923	</td>
4924	</tr>
4925	<tr>
4926	<td>
4927	<table cellspacing="0" cellpadding="4" width="100%" border="0">
4928	<tr>
4929	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4930	Syntax<p> </p>
4931	</th>
4932	<td class="code" valign="top" nowrap width="100%"><code>diagnostics
4933	= solvesdp(F,h,ops)</code></td>
4934	</tr>
4935	<tr>
4936	<td class="tabxpl">
4937	<table border="0">
4938	<tr>
4939	<td>
4940	<p align="right"><font face="Courier New" size="2">diagnostic:</font></p>
4941	</td>
4942	<td>Output structure</td>
4943	</tr>
4944	<tr>
4945	<td>
4946	<p align="right"><font face="Courier New" size="2">F:</font></p>
4947	</td>
4948	<td>set object describing the constraints. Can be [].</td>
4949	</tr>
4950	<tr>
4951	<td>
4952	<p align="right"><font face="Courier New" size="2">h:</font></p>
4953	</td>
4954	<td>sdpvar-object describing the objective function. Can be [].</td>
4955	</tr>
4956	<tr>
4957	<td>
4958	<p align="right"><font face="Courier New" size="2">ops:</font></p>
4959	</td>
4960	<td>options structure from sdpsettings. Can be [].</td>
4961	</tr>
4962	</table>
4963	</td>
4964	</tr>
4965	<tr>
4966	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4967	Description</th>
4968	</tr>
4969	<tr>
4970	<td class="tabxpl">solvesdp is the common function for solving all
4971	optimization problems.</td>
4972	</tr>
4973	<tr>
4974	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
4975	Examples</th>
4976	</tr>
4977	<tr>
4978	<td class="tabxpl">A linear program <font face="Tahoma"><b>{min c'x
4979	</b>subject to<b> Ax<= b}</b></font> can be solved with the following
4980	piece of code<table cellpadding="10" width="100%">
4981	<tr>
4982	<td class="xmpcode">
4983	<pre>x = sdpvar(length(c),1);
4984	F = set(A*x<b)
4985	solvesdp(F,c'*x);</pre>
4986	</td>
4987	</tr>
4988	</table>
4989	<p>If we only look for a feasible solution, we can omit the objective
4990	function </p>
4991	<table cellpadding="10" width="100%">
4992	<tr>
4993	<td class="xmpcode">
4994	<pre>solvesdp(F);</pre>
4995	</td>
4996	</tr>
4997	</table>
4998	<p>Solving the feasibility problem with the solver
4999	<a href="solvers.htm#quadprog">QUADPROG</a> can be done with </p>
5000	<table cellpadding="10" width="100%">
5001	<tr>
5002	<td class="xmpcode">
5003	<pre>solvesdp(F,[],sdpsettings('solver','quadprog'));</pre>
5004	</td>
5005	</tr>
5006	</table>
5007	<p>Minimizing an objective function is done by passiing a second argument</p>
5008	<table cellpadding="10" width="100%">
5009	<tr>
5010	<td class="xmpcode">
5011	<pre>solvesdp(F,sum(x));</pre>
5012	</td>
5013	</tr>
5014	</table>
5015	<p>For more examples, run <a href="reference.htm#yalmipdemo">yalmipdemo</a>
5016	and check out all the
5017	<a target="contents" href="mnl_cnt_examples.htm">examples</a>.</p>
5018	</td>
5019	</tr>
5020	<tr>
5021	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5022	Related commands</th>
5023	</tr>
5024	<tr>
5025	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>,
5026	<a href="reference.htm#set">set</a>,
5027	<a href="reference.htm#logdet">logdet</a>,
5028	<a href="reference.htm#sdpsettings">sdpsettings</a>,
5029	<a href="reference.htm#solvemoment">solvemoment</a>,
5030	<a href="reference.htm#solvemp">solvemp</a>,
5031	<a href="reference.htm#solvesos">solvesos</a></td>
5032	</tr>
5033	</table>
5034	</td>
5035	</tr>
5036	</table>
5037	<p> </p>
5038	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
5039	<tr>
5040	<td class="tableheader">
5041	<p class="tableheader"><a name="solvesos">SOLVESOS</a></p>
5042	</td>
5043	</tr>
5044	<tr>
5045	<td>
5046	<table cellspacing="0" cellpadding="4" width="100%" border="0">
5047	<tr>
5048	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5049	Syntax<p> </p>
5050	</th>
5051	<td class="code" valign="top" nowrap width="100%"><code>[sol,m,B]
5052	= solvesos(F,h,options,params)</code></td>
5053	</tr>
5054	<tr>
5055	<td class="tabxpl">
5056	<table border="0">
5057	<tr>
5058	<td>
5059	<p align="right"><font face="Courier New" size="2">sol:</font></p>
5060	</td>
5061	<td>diagnostics structure from solvesdp</td>
5062	</tr>
5063	<tr>
5064	<td>
5065	<p align="right"><font face="Courier New" size="2">m:</font></p>
5066	</td>
5067	<td>sdpvar object</td>
5068	</tr>
5069	<tr>
5070	<td>
5071	<p align="right"><font face="Courier New" size="2">B:</font></p>
5072	</td>
5073	<td>cell with double</td>
5074	</tr>
5075	<tr>
5076	<td>
5077	<p align="right"><font face="Courier New" size="2">F:</font></p>
5078	</td>
5079	<td>set object (Constraints on parametric variables and SOS constraints)</td>
5080	</tr>
5081	<tr>
5082	<td>
5083	<p align="right"><font face="Courier New" size="2">h:</font></p>
5084	</td>
5085	<td>sdpvar object (Objective function)</td>
5086	</tr>
5087	<tr>
5088	<td>
5089	<p align="right"><font face="Courier New" size="2">options:</font></p>
5090	</td>
5091	<td>structure from sdpsettings</td>
5092	</tr>
5093	<tr>
5094	<td><font face="Courier New" size="2">params:</font></td>
5095	<td>sdpvar object (The parametric variables)</td>
5096	</tr>
5097	</table>
5098	</td>
5099	</tr>
5100	<tr>
5101	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5102	Description</th>
5103	</tr>
5104	<tr>
5105	<td class="tabxpl">solvesos calculates SOS (sum-of-squares) decompositions.</td>
5106	</tr>
5107	<tr>
5108	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5109	Examples</th>
5110	</tr>
5111	<tr>
5112	<td class="tabxpl">In its most simple form,
5113	<a href="reference.htm#solvesos">solvesos</a> takes a SOS constrained
5114	polynomial and calculates the SOS decomposition.<table cellpadding="10" width="100%">
5115	<tr>
5116	<td class="xmpcode">
5117	<pre>x = sdpvar(1,1);
5118	p = x^4+x+5;
5119	F = set(sos(p)); % Constrain p to be a SOS
5120	solvesos(F);</pre>
5121	</td>
5122	</tr>
5123	</table>
5124	<p>The SOS-decompositions should give <strong>p(x)=v(x)<sup>T</sup>v(x)</strong>
5125	</p>
5126	<table cellpadding="10" width="100%">
5127	<tr>
5128	<td class="xmpcode">
5129	<pre>v = sosd(F);
5130	sdisplay(p-v'*v)
5131	<font color="#000000">ans = </font></pre>
5132	<pre><font color="#000000"> '-1.7764e-015+7.7716e-016x-1.1102e-015x^4'</font></pre>
5133	</td>
5134	</tr>
5135	</table>
5136	<p>Obviously, not entirely true. However the coefficients are small
5137	and most likely due to numerical inaccuracy. Remove all terms with
5138	coeffients smaller than 1e-6 using the command
5139	<a href="reference.htm#clean">clean</a> </p>
5140	<table cellpadding="10" width="100%">
5141	<tr>
5142	<td class="xmpcode">
5143	<pre>sdisplay(clean(p-v'*v,1e-6))
5144	<font color="#000000">ans =
5145	'0'</font></pre>
5146	</td>
5147	</tr>
5148	</table>
5149	<p>Parameterized SOS problems  are also possible. As an example,
5150	a lower bound on the global minimum of <b><font face="Tahoma">p</font></b>
5151	is obtained by finding a SOS decomposition of <b>
5152	<font face="Tahoma">p-t</font></b>, while maximizing <b>
5153	<font face="Tahoma">t</font></b>. The full syntax is </p>
5154	<table cellpadding="10" width="100%">
5155	<tr>
5156	<td class="xmpcode">
5157	<pre>t = sdpvar(1,1);
5158	F = set(sos(p-t));
5159	solvesos(F,-t,[],t);
5160	double(t)
5161	<font color="#000000">ans =</font></pre>
5162	<pre><font color="#000000"> 4.5275</font></pre>
5163	</td>
5164	</tr>
5165	</table>
5166	<p>Parametric variables (the last argument in the code above) are
5167	automatically detected if they are part of the objective function
5168	or part of non-SOS constraints. Hence, the problem above can be simplified.</p>
5169	<table cellpadding="10" width="100%">
5170	<tr>
5171	<td class="xmpcode">
5172	<pre>t = sdpvar(1,1);
5173	F = set(sos(p-t));
5174	solvesos(F,-t);
5175	double(t)
5176	<font color="#000000">ans =</font></pre>
5177	<pre><font color="#000000"> 4.5275</font></pre>
5178	</td>
5179	</tr>
5180	</table>
5181	<p>For more examples, run <a href="reference.htm#yalmipdemo">yalmipdemo</a>
5182	and check out the <a target="contents" href="mnl_cnt_examples.htm">
5183	examples</a> in this manual.</p>
5184	</td>
5185	</tr>
5186	<tr>
5187	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5188	Related commands</th>
5189	</tr>
5190	<tr>
5191	<td class="tabxpl"><a href="reference.htm#sdpvar">sdpvar</a>,
5192	<a href="reference.htm#solvesdp">solvesdp</a>,
5193	<a href="reference.htm#solvemoment">solvemoment</a>,
5194	<a href="reference.htm#sdisplay">sdisplay</a>,
5195	<a href="reference.htm#clean">clean</a></td>
5196	</tr>
5197	</table>
5198	</td>
5199	</tr>
5200	</table>
5201	<p> </p>
5202	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
5203	<tr>
5204	<td class="tableheader">
5205	<p class="tableheader"><a name="sos">SOS</a></p>
5206	</td>
5207	</tr>
5208	<tr>
5209	<td>
5210	<table cellspacing="0" cellpadding="4" width="100%" border="0">
5211	<tr>
5212	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5213	Syntax</th>
5214	<td class="code" valign="top" nowrap width="100%"><code>s = sos(p)</code></td>
5215	</tr>
5216	<tr>
5217	<td class="tabxpl">
5218	<table border="0">
5219	<tr>
5220	<td>
5221	<p align="right">s:</p>
5222	</td>
5223	<td>sdpvar object (only useful in <a href="reference.htm#lmi">
5224	set</a>)</td>
5225	</tr>
5226	<tr>
5227	<td>
5228	<p align="right">p:</p>
5229	</td>
5230	<td>polynomial scalar sdpvar object</td>
5231	</tr>
5232	</table>
5233	</td>
5234	</tr>
5235	<tr>
5236	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5237	Description</th>
5238	</tr>
5239	<tr>
5240	<td class="tabxpl">sos is used to define sum-of-squares (SOS) constraints</td>
5241	</tr>
5242	<tr>
5243	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5244	Examples</th>
5245	</tr>
5246	<tr>
5247	<td class="tabxpl">Solving a simple SOS problem and extracting the
5248	decomposition is done as<table cellpadding="10" width="100%">
5249	<tr>
5250	<td class="xmpcode">
5251	<pre>x = sdpvar(1,1);
5252	p = x^8+x^7+1;
5253	F = set(sos(p));
5254	solvesos(F);
5255	sdisplay(sosd(F))</pre>
5256	<pre><font color="#000000">ans = </font></pre>
5257	<pre><font color="#000000"> '0.12828-0.062411x+0.12427x^2-0.49555x^3-0.99602x^4'
5258	'0.99174+0.008073x-0.018071x^2+0.072068x^3+0.089115x^4'</font></pre>
5259	</td>
5260	</tr>
5261	</table>
5262	</td>
5263	</tr>
5264	<tr>
5265	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5266	Related commands</th>
5267	</tr>
5268	<tr>
5269	<td class="tabxpl"><a href="reference.htm#solvesos">solvesos</a>,
5270	<a href="reference.htm#sdpvar">sdpvar</a>,
5271	<a href="reference.htm#sosd">sosd</a></td>
5272	</tr>
5273	</table>
5274	</td>
5275	</tr>
5276	</table>
5277	<p> </p>
5278	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
5279	<tr>
5280	<td class="tableheader">
5281	<p class="tableheader"><a name="sosd">SOSD</a></p>
5282	</td>
5283	</tr>
5284	<tr>
5285	<td>
5286	<table cellspacing="0" cellpadding="4" width="100%" border="0">
5287	<tr>
5288	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5289	Syntax</th>
5290	<td class="code" valign="top" nowrap width="100%"><code>v = sosd(F)</code></td>
5291	</tr>
5292	<tr>
5293	<td class="tabxpl">
5294	<table border="0">
5295	<tr>
5296	<td>
5297	<p align="right"><font face="Courier New">v:</font></p>
5298	</td>
5299	<td>sdpvar object</td>
5300	</tr>
5301	<tr>
5302	<td>
5303	<p align="right"><font face="Courier New">F:</font></p>
5304	</td>
5305	<td>set object with a <a href="reference.htm#sos">sos</a> constraint</td>
5306	</tr>
5307	</table>
5308	</td>
5309	</tr>
5310	<tr>
5311	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5312	Description</th>
5313	</tr>
5314	<tr>
5315	<td class="tabxpl">sosd is used to extract the SOS decomposition from
5316	a sum-of-squares (SOS) constraint.</td>
5317	</tr>
5318	<tr>
5319	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5320	Examples</th>
5321	</tr>
5322	<tr>
5323	<td class="tabxpl">Solving a simple SOS problem and extracting the
5324	decomposition is done as<table cellpadding="10" width="100%">
5325	<tr>
5326	<td class="xmpcode">
5327	<pre>x = sdpvar(1,1);
5328	p = x^8+x^7+1;
5329	F = set(sos(p));
5330	solvesos(F);
5331	sdisplay(sosd(F))</pre>
5332	<pre><font color="#000000">ans = </font></pre>
5333	<pre><font color="#000000"> '0.12828-0.062411x+0.12427x^2-0.49555x^3-0.99602x^4'
5334	'0.99174+0.008073x-0.018071x^2+0.072068x^3+0.089115x^4'</font></pre>
5335	</td>
5336	</tr>
5337	</table>
5338	</td>
5339	</tr>
5340	<tr>
5341	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5342	Related commands</th>
5343	</tr>
5344	<tr>
5345	<td class="tabxpl"><a href="reference.htm#solvesos">solvesos</a>,
5346	<a href="reference.htm#sdpvar">sdpvar</a>,
5347	<a href="reference.htm#sos">sos</a></td>
5348	</tr>
5349	</table>
5350	</td>
5351	</tr>
5352	</table>
5353	<p> </p>
5354	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
5355	<tr>
5356	<td class="tableheader">
5357	<p class="tableheader"><a name="sparse">SPARSE</font></a></p>
5358	</td>
5359	</tr>
5360	<tr>
5361	<td>
5362	<table cellspacing="0" cellpadding="4" width="100%" border="0">
5363	<tr>
5364	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5365	Syntax</th>
5366	<td class="code" valign="top" nowrap width="100%"><code>x = sparse(i,j,s,n,m)</code></td>
5367	</tr>
5368	<tr>
5369	<td class="tabxpl">
5370	<table border="0" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" cellspacing="0">
5371	<tr>
5372	<td>
5373	<p align="right"><font face="Courier New" size="2">x:</font></p>
5374	</td>
5375	<td>sdpvar object</td>
5376	</tr>
5377	<tr>
5378	<td>
5379	<p align="right"><font face="Courier New">i</font><font face="Courier New" size="2">:</font></p>
5380	</td>
5381	<td>double </td>
5382	</tr>
5383	<tr>
5384	<td>
5385	<p align="right"><font face="Courier New">j</font><font face="Courier New" size="2">:</font></p>
5386	</td>
5387	<td>double</td>
5388	</tr>
5389	<tr>
5390	<td>
5391	<p align="right"><font face="Courier New">s</font><font face="Courier New" size="2">:</font></p>
5392	</td>
5393	<td>sdpvar object</td>
5394	</tr>
5395	<tr>
5396	<td>
5397	<p align="right"><font face="Courier New">n</font><font face="Courier New" size="2">:</font></p>
5398	</td>
5399	<td>sdpvar object</td>
5400	</tr>
5401	<tr>
5402	<td><font face="Courier New">m:</font></td>
5403	<td>double</td>
5404	</tr>
5405	</table>
5406	</td>
5407	</tr>
5408	<tr>
5409	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5410	Description</th>
5411	</tr>
5412	<tr>
5413	<td class="tabxpl">sparse is used to create <font color="#0000ff">
5414	<a href="reference.htm#sdpvar">
5415	sdpvar</a> </font>objects  with a certain structure.</td>
5416	</tr>
5417	<tr>
5418	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5419	Examples</th>
5420	</tr>
5421	<tr>
5422	<td class="tabxpl">Creating a diagonal matrix with every second diagonal
5423	element zero can be done as<table cellpadding="10" width="100%">
5424	<tr>
5425	<td class="xmpcode">
5426	<pre>x = sparse(1:2:2n,1:2:2n,sdpvar(n,1))</pre>
5427	</td>
5428	</tr>
5429	</table>
5430	</td>
5431	</tr>
5432	<tr>
5433	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5434	Related commands</th>
5435	</tr>
5436	<tr>
5437	<td class="tabxpl"><a href="reference.htm#sdpvar">
5438	sdpvar</a></td>
5439	</tr>
5440	</table>
5441	</td>
5442	</tr>
5443	</table>
5444	<p> </p>
5445	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933" id="table60">
5446	<tr>
5447	<td class="tableheader">
5448	<p class="tableheader"><a name="unblkdiag">UNBLKDIAG</font></a></p>
5449	</td>
5450	</tr>
5451	<tr>
5452	<td>
5453	<table cellspacing="0" cellpadding="4" width="100%" border="0" id="table61">
5454	<tr>
5455	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5456	Syntax</th>
5457	<td class="code" valign="top" nowrap width="100%"><code>F =
5458	unblkdiag(X)</code></td>
5459	</tr>
5460	<tr>
5461	<td class="tabxpl">
5462	<table border="0" style="border-collapse: collapse" bordercolor="#111111" cellpadding="0" cellspacing="0" id="table62">
5463	<tr>
5464	<td>
5465	<p align="right"><font face="Courier New" size="2">F:</font></p>
5466	</td>
5467	<td>set object or cell with sdpvar objects</td>
5468	</tr>
5469	<tr>
5470	<td>
5471	<p align="right"><font face="Courier New" size="2">X:</font></p>
5472	</td>
5473	<td>set object </td>
5474	</tr>
5475	</table>
5476	</td>
5477	</tr>
5478	<tr>
5479	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5480	Description</th>
5481	</tr>
5482	<tr>
5483	<td class="tabxpl">unblkdiag is used to detect and extract block
5484	diagonal terms.</td>
5485	</tr>
5486	<tr>
5487	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5488	Examples</th>
5489	</tr>
5490	<tr>
5491	<td class="tabxpl">Create a block diagonal matrix<table cellpadding="10" width="100%" id="table63">
5492	<tr>
5493	<td class="xmpcode">
5494	<pre>A = sdpvar(2,2);
5495	B = sdpvar(3,3);
5496	C = diag(sdpvar(3,1));
5497	X = blkdiag(A,B,C);</pre>
5498	</td>
5499	</tr>
5500	</table>
5501	<p>Now destroy the block diagonal structure</p>
5502	<table cellpadding="10" width="100%" id="table64">
5503	<tr>
5504	<td class="xmpcode">
5505	<pre>p = randperm(8);
5506	X = X(p,p);
5507	spy(X)</pre>
5508	</td>
5509	</tr>
5510	</table>
5511	<p>The blocks are easily recovered (note that scalar terms are
5512	returned one by one)</p>
5513	<table cellpadding="10" width="100%" id="table65">
5514	<tr>
5515	<td class="xmpcode">
5516	<pre>blocks = unblkdiag(X)
5517	[3x3 sdpvar] [1x1 sdpvar] [2x2 sdpvar] [1x1 sdpvar] [1x1 sdpvar]</pre>
5518	</td>
5519	</tr>
5520	</table>
5521	<p>The command is most efficiently used on
5522	<a href="reference.htm#set">
5523	set</a> objects (the function will go through all
5524	constraints in the <a href="reference.htm#set">
5525	set</a> object and try to detect blocked terms)</p>
5526	<table cellpadding="10" width="100%" id="table66">
5527	<tr>
5528	<td class="xmpcode">
5529	<pre>F = set(X);
5530	F = unblkdiag(F)
5531	+++++++++++++++++++++++++++++++++++++++++++++++++
5532	\| ID\| Constraint\| Type\|
5533	+++++++++++++++++++++++++++++++++++++++++++++++++
5534	\| #1\| Numeric value\| Matrix inequality 3x3\|
5535	\| #2\| Numeric value\| Matrix inequality 2x2\|
5536	\| #3\| Numeric value\| Element-wise 3x1\|
5537	+++++++++++++++++++++++++++++++++++++++++++++++++</pre>
5538	</td>
5539	</tr>
5540	</table>
5541	</td>
5542	</tr>
5543	<tr>
5544	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5545	Related commands</th>
5546	</tr>
5547	<tr>
5548	<td class="tabxpl"> <a href="reference.htm#sdpvar">
5549	sdpvar</a>, <a href="reference.htm#dissect">
5550	dissect</a></td>
5551	</tr>
5552	</table>
5553	</td>
5554	</tr>
5555	</table>
5556	<p> </p>
5557	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
5558	<tr>
5559	<td class="tableheader">
5560	<p class="tableheader"><a name="yalmip">YALMIP</a></p>
5561	</td>
5562	</tr>
5563	<tr>
5564	<td>
5565	<table cellspacing="0" cellpadding="4" width="100%" border="0">
5566	<tr>
5567	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5568	Syntax</th>
5569	<td class="code" valign="top" nowrap width="100%"><code>yalmip(command)</code></td>
5570	</tr>
5571	<tr>
5572	<td class="tabxpl">
5573	<table border="0">
5574	<tr>
5575	<td><font face="Courier New">command</font><font face="Courier New" size="2">:</font></td>
5576	<td>char {'clear','info','version'}</td>
5577	</tr>
5578	</table>
5579	</td>
5580	</tr>
5581	<tr>
5582	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5583	Description</th>
5584	</tr>
5585	<tr>
5586	<td class="tabxpl">yalmip can be used to perform some adminstrative
5587	stuff.</td>
5588	</tr>
5589	<tr>
5590	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5591	Examples</th>
5592	</tr>
5593	<tr>
5594	<td class="tabxpl">To clear the internals of YALMIP<table cellpadding="10" width="100%">
5595	<tr>
5596	<td class="xmpcode">
5597	<pre>yalmip('clear')</pre>
5598	</td>
5599	</tr>
5600	</table>
5601	<p>Version number and release-date can be obtained</p>
5602	<table cellpadding="10" width="100%">
5603	<tr>
5604	<td class="xmpcode">
5605	<pre>[vernum,reldate] = yalmip('version');</pre>
5606	</td>
5607	</tr>
5608	</table>
5609	<p>Additional information can be displayed using the 'info' tag</p>
5610	<table cellpadding="10" width="100%">
5611	<tr>
5612	<td class="xmpcode">
5613	<pre>ver = yalmip('info')
5614	<font color="#000000">**********************************
5615	- - - - YALMIP 3 - - - - - - - - -
5616	**********************************
5617
5618	Variable Size
5619	No SDPVAR objects found
5620
5621	SET
5622	No SET objects found</font>
5623	</pre>
5624	</td>
5625	</tr>
5626	</table>
5627	</td>
5628	</tr>
5629	<tr>
5630	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5631	Related commands</th>
5632	</tr>
5633	<tr>
5634	<td class="tabxpl"><a href="reference.htm#sdpsettings">sdpsettings</a></td>
5635	</tr>
5636	</table>
5637	</td>
5638	</tr>
5639	</table>
5640	<p> </p>
5641	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
5642	<tr>
5643	<td class="tableheader">
5644	<p class="tableheader"><a name="yalmipdemo">YALMIPDEMO</font></a></p>
5645	</td>
5646	</tr>
5647	<tr>
5648	<td>
5649	<table cellspacing="0" cellpadding="4" width="100%" border="0">
5650	<tr>
5651	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2"> </th>
5652	<td class="code" valign="top" nowrap width="100%"><code>yalmipdemo</code></td>
5653	</tr>
5654	<tr>
5655	<td class="tabxpl"> </td>
5656	</tr>
5657	<tr>
5658	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5659	Description</th>
5660	</tr>
5661	<tr>
5662	<td class="tabxpl">yalmipdemo runs a set of tutorial problems</td>
5663	</tr>
5664	<tr>
5665	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5666	Examples</th>
5667	</tr>
5668	<tr>
5669	<td class="tabxpl">To start the tutorial<table cellpadding="10" width="100%">
5670	<tr>
5671	<td class="xmpcode">
5672	<pre>yalmipdemo</pre>
5673	</td>
5674	</tr>
5675	</table>
5676	</td>
5677	</tr>
5678	<tr>
5679	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5680	Related commands</th>
5681	</tr>
5682	<tr>
5683	<td class="tabxpl"><a href="#yalmiptest">yalmiptest</a></td>
5684	</tr>
5685	</table>
5686	</td>
5687	</tr>
5688	</table>
5689	<p> </p>
5690	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
5691	<tr>
5692	<td class="tableheader">
5693	<p class="tableheader"><a name="yalmiperror">YALMIPERROR</a></p>
5694	</td>
5695	</tr>
5696	<tr>
5697	<td>
5698	<table cellspacing="0" cellpadding="4" width="100%" border="0">
5699	<tr>
5700	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5701	Syntax</th>
5702	<td class="code" valign="top" nowrap width="100%"><code>yalmiperror(x)</code></td>
5703	</tr>
5704	<tr>
5705	<td class="tabxpl">
5706	<table border="0">
5707	<tr>
5708	<td><font face="Courier New" size="2">x:</font></td>
5709	<td>double</td>
5710	</tr>
5711	</table>
5712	</td>
5713	</tr>
5714	<tr>
5715	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5716	Description</th>
5717	</tr>
5718	<tr>
5719	<td class="tabxpl">yalmiperror returns the error-text for a error-code.</td>
5720	</tr>
5721	<tr>
5722	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5723	Examples</th>
5724	</tr>
5725	<tr>
5726	<td class="tabxpl">To se all available error codes,<table cellpadding="10" width="100%">
5727	<tr>
5728	<td class="xmpcode">
5729	<pre>yalmiperror
5730
5731	<font color="#000000"> Error codes
5732
5733	-5 License problems in solver
5734	-4 Solver not applicable
5735	-3 Solver not found
5736	-2 No suitable solver
5737	-1 Unknown error
5738	0 No problems detected
5739	1 Infeasible problem
5740	2 Unbounded objective function
5741	3 Maximum iterations exceeded
5742	4 Numerical problems
5743	5 Lack of progress
5744	6 Initial solution infeasible
5745	7 YALMIP sent incorrect input to solver
5746	8 Feasibility cannot be determined
5747	9 Unknown problem in solver
5748	10 bigM failed (increase sp.Mfactor)
5749	11 Other identified error
5750	12 Infeasible or unbounded
5751	13 YALMIP cannot determine status in solver</font></pre>
5752	</td>
5753	</tr>
5754	</table>
5755	<p>To see a particular error message, </p>
5756	<table cellpadding="10" width="100%">
5757	<tr>
5758	<td class="xmpcode">
5759	<pre>yalmiperror(3)
5760	<font color="#000000"> ans =</font></pre>
5761	<pre><font color="#000000"> Maximum iterations exceeded</font> </pre>
5762	</td>
5763	</tr>
5764	</table>
5765	</td>
5766	</tr>
5767	<tr>
5768	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5769	Related commands</th>
5770	</tr>
5771	<tr>
5772	<td class="tabxpl"><a href="reference.htm#solvesdp">solvesdp</a></td>
5773	</tr>
5774	</table>
5775	</td>
5776	</tr>
5777	</table>
5778	<p> </p>
5779	<table border="1" cellpadding="0" cellspacing="0" style="border-collapse: collapse" width="100%" bordercolor="#FF9933">
5780	<tr>
5781	<td class="tableheader">
5782	<p class="tableheader"><a name="yalmiptest">YALMIPTEST</a></p>
5783	</td>
5784	</tr>
5785	<tr>
5786	<td>
5787	<table cellspacing="0" cellpadding="4" width="100%" border="0">
5788	<tr>
5789	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5790	Syntax</th>
5791	<td class="code" valign="top" nowrap width="100%"><code>yalmiptest(ops)</code></td>
5792	</tr>
5793	<tr>
5794	<td class="tabxpl">
5795	<table border="0">
5796	<tr>
5797	<td><font face="Courier New" size="2">ops:</font></td>
5798	<td>sdpsettings structure</td>
5799	</tr>
5800	</table>
5801	</td>
5802	</tr>
5803	<tr>
5804	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5805	Description</th>
5806	</tr>
5807	<tr>
5808	<td class="tabxpl">yalmiptest runs a set of test examples to test
5809	the installation</td>
5810	</tr>
5811	<tr>
5812	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5813	Examples</th>
5814	</tr>
5815	<tr>
5816	<td class="tabxpl">To test the default installation<table cellpadding="10" width="100%">
5817	<tr>
5818	<td class="xmpcode">
5819	<pre>yalmiptest</pre>
5820	</td>
5821	</tr>
5822	</table>
5823	<p>To test a particular solver </p>
5824	<table cellpadding="10" width="100%">
5825	<tr>
5826	<td class="xmpcode">
5827	<pre>yalmiptest(sdpsettings('solver','sdpt3'))</pre>
5828	</td>
5829	</tr>
5830	</table>
5831	</td>
5832	</tr>
5833	<tr>
5834	<th class="doc" valign="top" nowrap align="left" bgcolor="#eeeeee" rowspan="2">
5835	Related commands</th>
5836	</tr>
5837	<tr>
5838	<td class="tabxpl"><a href="reference.htm#sdpsettings">sdpsettings</a></td>
5839	</tr>
5840	</table>
5841	</td>
5842	</tr>
5843	</table>
5844	<p> </p>
5845	<p> </p>
5846	<p> </p>
5847	<p> </p>
5848	<p> </p>
5849	<p> </p>
5850	<p> </p>
5851	<p> </p>
5852	<p> </p>
5853	<p> </p>
5854	<p> </p>
5855	<p> </p>
5856	<p> </p>
5857	<p> </p>
5858	<p> </p>
5859	<p> </p>
5860	<p> </p>
5861	<p> </p>
5862	<p> </p>
5863	</td>
5864	</tr>
5865	</table>
5866	</div>
5867
5868	</body>
5869
5870	</html>

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