1 | function [Fdual,objdual,y,X] = primalize(F,obj) |
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2 | % PRIMALIZE Create the dual of an SDP given in dual form |
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3 | % |
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4 | % [Fd,objd,y] = primalize(F,obj) |
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5 | % |
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6 | % Input |
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7 | % F : Primal constraint in form C-Ay > 0, Fy = g |
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8 | % obj : Primal cost maximize b'y |
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9 | % |
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10 | % Output |
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11 | % Fd : Dual constraints in form X>0, Trace(AiX)==bi+dt |
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12 | % obj : Dual cost trace(CX) |
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13 | % y : The detected primal free variables |
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14 | % |
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15 | % Example |
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16 | % See the HTML help. |
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17 | % |
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18 | % See also DUAL, SOLVESDP, SDPVAR, DUALIZE |
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19 | |
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20 | % Author Johan Löfberg |
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21 | % $Id: primalize.m,v 1.5 2005/12/19 15:27:31 joloef Exp $ |
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22 | |
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23 | err = 0; |
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24 | |
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25 | % It's general, but not insanely general... |
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26 | if ~(islinear(F) & islinear(obj)) |
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27 | if nargout == 6 |
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28 | Fdual = set([]);objdual = [];y = []; err = 1; |
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29 | else |
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30 | error('Can only primalize linear problems'); |
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31 | end |
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32 | end |
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33 | if any(is(F,'socc')) |
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34 | if nargout == 6 |
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35 | Fdual = set([]);objdual = [];y = []; err = 1; |
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36 | else |
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37 | error('Cannot primalize second order cone constraints'); |
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38 | end |
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39 | end |
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40 | if isa(obj,'sdpvar') |
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41 | if any(is(F,'complex')) | is(obj,'complex') |
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42 | if nargout == 6 |
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43 | Fdual = set([]);objdual = [];y = []; X = []; t = []; err = 1; |
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44 | else |
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45 | error('Cannot primalize complex-valued problems'); |
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46 | end |
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47 | end |
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48 | end |
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49 | if any(is(F,'integer')) | any(is(F,'binary')) |
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50 | if nargout == 6 |
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51 | Fdual = set([]);objdual = [];y = []; err = 1; |
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52 | else |
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53 | error('Cannot primalize discrete problems'); |
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54 | end |
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55 | end |
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56 | |
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57 | % Create model using the standard code |
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58 | model = export(F,obj,sdpsettings('solver','sedumi')); |
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59 | |
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60 | Fdual = set([]); |
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61 | xvec = []; |
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62 | if model.K.f > 0 |
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63 | t = sdpvar(model.K.f,1); |
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64 | xvec = [xvec;t]; |
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65 | end |
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66 | |
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67 | if model.K.l > 0 |
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68 | x = sdpvar(model.K.l,1); |
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69 | xvec = [xvec;x]; |
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70 | Fdual = Fdual + set(x>0); |
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71 | end |
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72 | |
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73 | if model.K.q(1) > 0 |
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74 | for i = 1:length(model.K.q) |
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75 | x = sdpvar(model.K.q(i),1); |
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76 | xvec = [xvec;x]; |
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77 | Fdual = Fdual + set(cone(x(2:end),x(1))); |
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78 | end |
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79 | end |
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80 | |
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81 | if model.K.s(1)>0 |
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82 | for i = 1:length(model.K.s) |
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83 | X{i} = sdpvar(model.K.s(i),model.K.s(i)); |
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84 | xvec = [xvec;X{i}(:)]; |
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85 | Fdual = Fdual + set(X{i}>0); |
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86 | end |
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87 | end |
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88 | |
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89 | objdual = model.C(:)'*xvec; |
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90 | Fdual = Fdual + set(-model.b == model.A'*xvec); |
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91 | |
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92 | yvars = union(getvariables(F),getvariables(obj)); |
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93 | y = recover(yvars); |
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94 | |
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95 | yalmip('associatedual',getlmiid(Fdual(end)),y); |
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96 | |
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97 | |
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98 | |
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99 | |
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