1 | function regress_dualize |
---|
2 | |
---|
3 | |
---|
4 | ops = sdpsettings('verbose',0); |
---|
5 | |
---|
6 | % TEST 1 |
---|
7 | yalmip('clear') |
---|
8 | A = randn(3,3);A = -A*A'; |
---|
9 | P = sdpvar(3,3); |
---|
10 | t = sdpvar(1,1); |
---|
11 | y = sdpvar(1,1); |
---|
12 | F = set(A'*P+P*A < -eye(3)); |
---|
13 | F = F + set(P > A*A') + set(P(3,3)>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12); |
---|
14 | obj = trace(P)+y; |
---|
15 | |
---|
16 | fail = regresstest(F,obj,ops); |
---|
17 | regressreport('Test 1',fail) |
---|
18 | |
---|
19 | % TEST 2 |
---|
20 | yalmip('clear') |
---|
21 | A = randn(3,3);A = -A*A'; |
---|
22 | P = sdpvar(3,3); |
---|
23 | t = sdpvar(1,1); |
---|
24 | y = sdpvar(1,1); |
---|
25 | F = set(A'*P+P*A < -eye(3)); |
---|
26 | F = F + set(P > 0) + set(P(3,3)>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12); |
---|
27 | obj = trace(P)+y; |
---|
28 | |
---|
29 | fail = regresstest(F,obj,ops); |
---|
30 | regressreport('Test 2',fail) |
---|
31 | |
---|
32 | yalmip('clear') |
---|
33 | A = randn(3,3);A = -A*A'; |
---|
34 | P = sdpvar(3,3); |
---|
35 | t = sdpvar(1,1); |
---|
36 | y = sdpvar(1,1); |
---|
37 | F = set(A'*P+P*A < -eye(3)); |
---|
38 | F = F + set(P > 0) + set(P(3,3)>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>0); |
---|
39 | obj = trace(P)+y; |
---|
40 | |
---|
41 | fail = regresstest(F,obj,ops); |
---|
42 | regressreport('Test 3',fail) |
---|
43 | |
---|
44 | yalmip('clear') |
---|
45 | A = randn(3,3);A = -A*A'; |
---|
46 | P = sdpvar(3,3); |
---|
47 | t = sdpvar(1,1); |
---|
48 | y = sdpvar(1,1); |
---|
49 | F = set(A'*P+P*A < -eye(3)); |
---|
50 | F = F + set(P > 0) + set(P(3,3)>0) + set(t-y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>0); |
---|
51 | obj = trace(P); |
---|
52 | |
---|
53 | fail = regresstest(F,obj,ops); |
---|
54 | regressreport('Test 4',fail) |
---|
55 | |
---|
56 | yalmip('clear') |
---|
57 | X = sdpvar(3,3); |
---|
58 | x = sdpvar(3,1); |
---|
59 | obj = trace(X)+sum(x); |
---|
60 | F = set(X>0) + set(cone(x(2:end),x(1))) + set(trace(X)==x(1)+2*x(2)+3*x(3)+4)+set(X(1,3)==8); |
---|
61 | fail = regresstest(F,obj,ops); |
---|
62 | regressreport('Test 5',fail) |
---|
63 | |
---|
64 | yalmip('clear') |
---|
65 | X = sdpvar(3,3); |
---|
66 | x = sdpvar(3,1); |
---|
67 | obj = trace(X)+sum(x); |
---|
68 | F = set(X>0) + set(cone(x(2:end),1+x(1))) + set(trace(X)==x(1)+2*x(2)+3*x(3)+4)+set(X(1,3)==8); |
---|
69 | fail = regresstest(F,obj,ops); |
---|
70 | regressreport('Test 6',fail) |
---|
71 | |
---|
72 | yalmip('clear') |
---|
73 | X = sdpvar(3,3); |
---|
74 | x = sdpvar(3,1); |
---|
75 | obj = trace(X)+sum(x); |
---|
76 | F = set(X>0) + set(cone(x(2:end),1+x(1))) + set(trace(X)==x(1)+2*x(2)+3*x(3)+4)+set(X(1,3)==8); |
---|
77 | fail = regresstest(F,obj,ops); |
---|
78 | regressreport('Test 7',fail) |
---|
79 | |
---|
80 | yalmip('clear') |
---|
81 | X = sdpvar(3,3); |
---|
82 | x = sdpvar(3,1); |
---|
83 | obj = trace(X)+sum(x); |
---|
84 | F = set(X>0) + set(cone(1-x(2:end),1+x(1))) + set(trace(X)==x(1)+2*x(2)+3*x(3)+4)+set(X(1,3)==8); |
---|
85 | fail = regresstest(F,obj,ops); |
---|
86 | regressreport('Test 8',fail) |
---|
87 | |
---|
88 | yalmip('clear') |
---|
89 | A = randn(3,3);A = -A*A'; |
---|
90 | P = sdpvar(3,3); |
---|
91 | t = sdpvar(1,1); |
---|
92 | y = sdpvar(1,1); |
---|
93 | F = set(A'*P+P*A < -eye(3)); |
---|
94 | F = F + set(P > A*A') + set(P(3,3)>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12)+set(t>-12); |
---|
95 | obj = trace(P)+y; |
---|
96 | fail = regresstest(F,obj,ops); |
---|
97 | regressreport('Test 9',fail) |
---|
98 | |
---|
99 | %yalmip('clear') |
---|
100 | A = randn(3,3);A = -A*A'; |
---|
101 | P = sdpvar(3,3); |
---|
102 | %t = sdpvar(1,1); |
---|
103 | %y = sdpvar(1,1); |
---|
104 | F = set(A'*P+P*A < -eye(3)); |
---|
105 | F = F + set(P > A*A') + set(P(3,3)>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12)+set(t>-12); |
---|
106 | obj = trace(P)+y+t; |
---|
107 | fail = regresstest(F,obj,ops); |
---|
108 | regressreport('Test 10',fail) |
---|
109 | |
---|
110 | yalmip('clear') |
---|
111 | A = randn(3,3);A = -A*A'; |
---|
112 | P = sdpvar(3,3); |
---|
113 | t = sdpvar(1,1); |
---|
114 | y = sdpvar(1,1); |
---|
115 | F = set(A'*P+P*A < -eye(3)); |
---|
116 | F = F + set(P > A*A') + set(P(3,3)>0) + set(P>0) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12)+set(t>-12); |
---|
117 | obj = trace(P)+y+t; |
---|
118 | fail = regresstest(F,obj,ops); |
---|
119 | regressreport('Test 11',fail) |
---|
120 | |
---|
121 | %yalmip('clear') |
---|
122 | A = randn(3,3);A = -A*A'; |
---|
123 | P = sdpvar(3,3); |
---|
124 | %t = sdpvar(1,1); |
---|
125 | y = sdpvar(1,1); |
---|
126 | F = set(A'*P+P*A < -eye(3)); |
---|
127 | F = F + set(P > A*A') + set(P(3,3)>0) + set(P>0) + set(t+y > 7) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12)+set(t>-12); |
---|
128 | obj = trace(P)+y+t; |
---|
129 | fail = regresstest(F,obj,ops); |
---|
130 | regressreport('Test 12',fail) |
---|
131 | |
---|
132 | yalmip('clear') |
---|
133 | A = randn(3,3);A = -A*A'; |
---|
134 | P = sdpvar(3,3); |
---|
135 | t = sdpvar(1,1); |
---|
136 | y = sdpvar(1,1); |
---|
137 | F = set(A'*P+P*A < -eye(3)); |
---|
138 | F = F + set(2*P > A*A') + set(P(3,3)>0) + set(P>0) + set(t+y > 7) + set(t+y > 7) + set(P(2,2)>4)+set(P(1,1:2)>t) + set(t>12)+set(t>-12); |
---|
139 | obj = trace(P)+y+t; |
---|
140 | fail = regresstest(F,obj,ops); |
---|
141 | regressreport('Test 13',fail) |
---|
142 | |
---|
143 | |
---|
144 | |
---|
145 | |
---|
146 | function regressreport(text,fail) |
---|
147 | |
---|
148 | switch fail |
---|
149 | case 0 |
---|
150 | disp(['No problems in ' text]); |
---|
151 | case 1 |
---|
152 | disp(['Objective differ in ' text]); |
---|
153 | case 2 |
---|
154 | disp(['Infeasible solution in ' text]); |
---|
155 | otherwise |
---|
156 | end |
---|
157 | |
---|
158 | |
---|
159 | function fail = regresstest(F,obj,ops); |
---|
160 | solvesdp(F,obj,ops); |
---|
161 | obj1 = double(obj); |
---|
162 | p1 = checkset(F); |
---|
163 | |
---|
164 | x = recover(getvariables(F)); |
---|
165 | setsdpvar(x,0*double(x)); |
---|
166 | |
---|
167 | [Fdual,objdual,X,free,err] = dualize(F,obj); |
---|
168 | solvesdp(Fdual,-objdual,ops); |
---|
169 | |
---|
170 | if length(X)>0 |
---|
171 | for i = 1:length(X);setsdpvar(X{i},dual(Fdual(i)));end |
---|
172 | end |
---|
173 | if ~isempty(free) |
---|
174 | setsdpvar(free,dual(Fdual(end))); |
---|
175 | end |
---|
176 | |
---|
177 | obj2 = double(obj); |
---|
178 | p2 = checkset(Fdual); |
---|
179 | |
---|
180 | fail = 0; |
---|
181 | |
---|
182 | if abs(obj1-obj2) > 1e-4 |
---|
183 | fail = 1; |
---|
184 | [obj1 obj2] |
---|
185 | end |
---|
186 | if any(p2<-1e-5) |
---|
187 | fail = 2; |
---|
188 | end |
---|
189 | |
---|