1 | function F = set(varargin) |
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2 | %SET Defines a constraint (the feasible set) |
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3 | % |
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4 | % F = SET([]) Creates an empty SET-object |
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5 | % F = SET(X > Y) Constrains X-Y to be positive semi-definite if X-Y is Hermitian, |
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6 | % interpreted as element-wise constraint otherwise |
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7 | % F = SET(X==Y) Element-wise equality constraint |
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8 | % F = SET(CONE(X,Y)) Second order cone constraint ||X||<Y (X column vector, Y scalar) |
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9 | % |
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10 | % Constraints can also be generated using string notation (displays nicely with syntax high-lightning) |
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11 | % F = SET('X>Y') Constrains X-Y to be positive semi-definite if X-Y is Hermitian, |
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12 | % interpreted as element-wise constraint otherwise |
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13 | % F = SET('X==Y') Element-wise equality constraint |
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14 | % F = SET('||X||<Y') Create second order cone constraint (X and Y column vectors) |
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15 | % F = SET('cone(X,Y)') Create second order cone constraint (X and Y column vectors) |
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16 | % |
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17 | % Variables can be constrained to be integer or binary |
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18 | % F = SET(INTEGER(X)) |
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19 | % F = SET(BINARY(X)) |
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20 | % |
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21 | % Multiple constraints are obtained with overloaded plus |
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22 | % F = SET(X > 0) + SET(CONE(X(:),1)) + SET(X(1,1) == 1/2) |
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23 | % |
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24 | % Double-sided constraint (and extensions) can easily be defined |
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25 | % The following two comands give equivalent problems |
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26 | % F = SET(X > 0 > Y > Z < 5 < W) |
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27 | % F = SET(X > 0) + SET(0 > Y) + SET(Y > Z) + SET(Z < 5) + set(5 < W) |
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28 | % |
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29 | % A constraint can be tagged with a name or description |
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30 | % F = SET(X > Y,'tag') Gives the constraint a description (used in display/checkset) |
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31 | % |
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32 | % General info |
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33 | % |
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34 | % The right-hand side and left-hand side can be interchanged. Supports {>,<,>=,<=,==}. |
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35 | % See FAQ for information on strict vs. non-strict inequalities. |
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36 | % |
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37 | % Any valid expression built using DOUBLEs & SDPVARs can be used on both sides. |
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38 | % |
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39 | % The advantage of using the string notation approach is that more information will be |
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40 | % shown when the SET is displayed (and in checkset) |
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41 | % |
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42 | % See also DUAL, SOLVESDP, INTEGER, BINARY |
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43 | |
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44 | |
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45 | |
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46 | if isa(varargin{1},'blkvar') |
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47 | varargin{1} = sdpvar(varargin{1}); |
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48 | end |
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49 | |
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50 | switch nargin |
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51 | case 0 |
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52 | F = lmi; |
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53 | case 1 |
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54 | F = lmi(varargin{1}); |
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55 | case 2 |
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56 | F = lmi(varargin{1},varargin{2}); |
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57 | case 3 |
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58 | F = lmi(varargin{1},varargin{1},varargin{3}); |
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59 | otherwise |
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60 | end |
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61 | |
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