96 lines
2.1 KiB
Mathematica
96 lines
2.1 KiB
Mathematica
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function [Fdual,objdual,y,X] = primalize(F,obj)
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% PRIMALIZE Create the dual of an SDP given in dual form
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%
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% [Fd,objd,y] = primalize(F,obj)
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%
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% Input
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% F : Primal constraint in form C-Ay > 0, Fy = g
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% obj : Primal cost maximize b'y
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%
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% Output
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% Fd : Dual constraints in form X>0, Trace(AiX)==bi+dt
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% obj : Dual cost trace(CX)
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% y : The detected primal free variables
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%
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% Example
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% See the HTML help.
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%
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% See also DUAL, SOLVESDP, SDPVAR, DUALIZE
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err = 0;
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if isa(F,'constraint')
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F = (F);
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end
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% It's general, but not insanely general...
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if ~(islinear(F) & islinear(obj))
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if nargout == 6
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Fdual = ([]);objdual = [];y = []; err = 1;
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else
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error('Can only primalize linear problems');
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end
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end
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if any(is(F,'socc'))
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if nargout == 6
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Fdual = ([]);objdual = [];y = []; err = 1;
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else
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error('Cannot primalize second order cone constraints');
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end
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end
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if isa(obj,'sdpvar')
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if any(is(F,'complex')) | is(obj,'complex')
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if nargout == 6
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Fdual = ([]);objdual = [];y = []; X = []; t = []; err = 1;
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else
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error('Cannot primalize complex-valued problems');
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end
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end
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end
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if any(is(F,'integer')) | any(is(F,'binary'))
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if nargout == 6
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Fdual = ([]);objdual = [];y = []; err = 1;
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else
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error('Cannot primalize discrete problems');
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end
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end
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% Create model using the standard code
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model = export(F,obj,sdpsettings('solver','sedumi'),[],[],1);
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Fdual = ([]);
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xvec = [];
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if model.K.f > 0
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t = sdpvar(model.K.f,1);
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xvec = [xvec;t];
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end
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if model.K.l > 0
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x = sdpvar(model.K.l,1);
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xvec = [xvec;x];
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Fdual = Fdual + (x>=0);
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end
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if model.K.q(1) > 0
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for i = 1:length(model.K.q)
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x = sdpvar(model.K.q(i),1);
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xvec = [xvec;x];
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Fdual = Fdual + (cone(x(2:end),x(1)));
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end
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end
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if model.K.s(1)>0
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for i = 1:length(model.K.s)
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X{i} = sdpvar(model.K.s(i),model.K.s(i));
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xvec = [xvec;X{i}(:)];
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Fdual = Fdual + (X{i}>=0);
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end
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end
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objdual = model.C(:)'*xvec;
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Fdual = Fdual + (-model.b == model.A'*xvec);
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yvars = union(getvariables(F),getvariables(obj));
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y = recover(yvars);
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yalmip('associatedual',getlmiid(Fdual(end)),y);
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