85 lines
2.1 KiB
Mathematica
85 lines
2.1 KiB
Mathematica
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function cut = disjunctivecut(varargin)
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%
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%
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% x = sdpvar(2,1);
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% A1 = randn(8,2);
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% b1 = rand(8,1)*2-A1*[3;3];
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% A2 = randn(8,2);
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% b2 = rand(8,1)*2-A2*[-3;3];
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% A3 = randn(8,2);
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% b3 = rand(8,1)*2-A3*[3;-3];
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% C1 = A1*x < b1;
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% C2 = A2*x < b2;
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% C3 = A3*x < b3;
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% cut = disjunctivecut(C1,C2,C3,[-8;0]);cut = disjunctivecut(C1,C2,C3,[-8;0]);
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% plot([cut,-10<x<10]);plot(hull(C1,C2,C3),x);plot(C1,[],'y');plot(C2,[],'y');plot(C3,[],'y')
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xstar = varargin{end};
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x = [];
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beta = sdpvar(1);
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alpha = sdpvar(length(xstar),1);
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for i = 1:nargin-1
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[Imodel,Iax1,Iax2,p{i}] = export(varargin{i},[],sdpsettings,[],[],0);
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neq(i) = p{i}.K.f;
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b{i} = -p{i}.F_struc(:,1);
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A{i} = p{i}.F_struc(:,2:end);
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mu{i} = sdpvar(length(b{i}),1);
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end
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Objective = alpha'*xstar-beta;
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Constraints = [-1<alpha<1];
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summu = 0;
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for i = 1:nargin-1
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summu = summu + sum(mu{i});
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Constraints = [Constraints,alpha' == mu{i}'*A{i}];
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Constraints = [Constraints,beta <= mu{i}'*b{i}];
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Constraints = [Constraints,mu{i}(p{i}.K.f+1:end)>0];
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end
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solvesdp(Constraints,Objective,sdpsettings('verbose',0));
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x = recover(p{1}.used_variables);
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cut = (-double(beta)+double(alpha)'*x >= 0);
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return
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%x = recover(sdpvar(C1));
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%[Imodel,Iax1,Iax2,p1] = export(C1,[],sdpsettings,[],[],0);
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%[Omodel,Oax1,Oax2,p2] = export(C2,[],sdpsettings,[],[],0);
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%neq1 = p1.K.f;
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%neq2 = p2.K.f;
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%e1 = p1.F_struc*[1;x];
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%e2 = p2.F_struc*[1;x];
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%Model1 = [e2(1+p1.K.f:end)>=0];
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%Model2 = [e2(1+p2.K.f:end)>=0];
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if 0
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Ab1 = getbase(sdpvar(Model1));
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Ab2 = getbase(sdpvar(Model2));
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b1 = -Ab1(:,1);
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A1 = Ab1(:,2:end);
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b2 = -Ab2(:,1);
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A2 = Ab2(:,2:end);
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b1 = -p1.F_struc(:,1);
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A1 = p1.F_struc(:,2:end);
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b2 = -p2.F_struc(:,1);
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A2 = p2.F_struc(:,2:end);
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end
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alpha = sdpvar(length(xstar),1);
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beta = sdpvar(1);
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mu1 = sdpvar(length(b1),1);
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mu2 = sdpvar(length(b2),1);
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Objective = alpha'*xstar-beta;
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Constraint = [alpha' == mu1'*A1,alpha' == mu2'*A2, beta <= mu1'*b1, beta <= mu2'*b2,mu1(neq1+1:end)>0,mu2(neq2+1:end)>0];
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Constraint = [Constraint,-1<alpha<1,sum(mu1)+sum(mu2)<10];
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solvesdp(Constraint,Objective,sdpsettings('verbose',0));
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cut = (-double(beta)+double(alpha)'*x >= 0);
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