67 lines
1.8 KiB
Mathematica
67 lines
1.8 KiB
Mathematica
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function [Fconv,info] = nonlineartocone(F)
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%NONLINEARTOCONE Convert nonlinear constraint to second order cone
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if islinear(F)
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Fconv = F;
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info = 0;
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return
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end
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[n,m]=size(F);
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if (n*m==1)
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Fconv = [];
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% Involved in polynomial constraints
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sqrList = yalmip('nonlinearvariables');
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h = sort(unique(sqrList));
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% % SDP relaxation
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for i = 1:size(sqrList,1)
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left_index = find(h==sqrList(i,1));
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x1_index = find(h==sqrList(i,2));
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x2_index = find(h==sqrList(i,3));
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Z{i}=zeros(length(h),length(h));
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if x1_index==x2_index
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Z{i}(x2_index,x1_index) = 1;
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else
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Z{i}(x1_index,x2_index) = 0.5;
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Z{i}(x2_index,x1_index) = 0.5;
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end
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end
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vars = getvariables(F);
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base = getbase(F);
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nonlinvars = find(ismember(vars,sqrList(:,1)));
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linvars = find(~ismember(vars,sqrList(:,1)));
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% Construct quadratic
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Q = zeros(length(h));
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for i = 1:length(nonlinvars)
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indexinlist = find(vars(nonlinvars(i))==sqrList(:,1));
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indexinh = find(vars(nonlinvars(i))==h);
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Q = Q-Z{indexinlist}*base(1+find(h(indexinh)==vars));
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end
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used = find(any(Q));
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[B,r] = chol(Q(used,used));
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if r==0
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linear = base(1);
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if ~isempty(linvars)
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linear = linear+base(1+find(ismember(linvars,vars)))*recover(linvars);
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end
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ConesAxb=[2*B*recover(h(used));1-linear];
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Conescxd=1+linear;
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Fconv = cone(ConesAxb,Conescxd);
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info = 0;
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else
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Fconv = F;
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if nargout == 2
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info = 1;
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else
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warning('Cannot re-write to second order cone constraint');
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end
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end
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else
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if nargout == 2
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Fconv = F;
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info = 1;
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else
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error('nonlineartocone can only be applied to scalar inequalities')
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end
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end
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