102 lines
2.5 KiB
Mathematica
102 lines
2.5 KiB
Mathematica
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function [dualUpper,L,U] = derivedualBoundsParameterFree(H,c,A,b,E,f,ops,parametricDomain)
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if isempty(A)
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dualUpper = [];
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L = [];
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U = [];
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return
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end
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n = length(c);
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m = length(b);
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me = length(f);
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x = sdpvar(n,1);
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Lambda = sdpvar(m,1);
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mu = sdpvar(me,1);
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% Homogenization
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alpha = sdpvar(1);
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F = [];
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% Start by computing primal lower bounds
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if nargin < 7
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ops = sdpsettings('verbose',0);
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end
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ops2 = ops;
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ops2.verbose = max(0,ops.verbose-1);;
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all_bounded = 1;
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if ops.verbose
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disp(['*Computing ' num2str(length(x)) ' primal bounds (required for dual bounds)']);
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end
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z = recover(unique([depends(c);depends(b)]));
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xz = [x;z];
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nz = length(z);
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nTOT = n + length(z);
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rhs = 0;
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if ~isempty(b)
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rhs = rhs + A'*Lambda;
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end
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if ~isempty(f)
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rhs = rhs + E'*mu;
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end
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[c0,C] = deParameterize(c,z);
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[b0,B] = deParameterize(b,z);
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delta = binvar(length(b),1);
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UpperBound = .1;
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parametricDomainH = homogenize(sdpvar(parametricDomain),alpha) >= 0;
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w1 = binvar(length(Lambda),1);
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w2 = binvar(length(Lambda),1);
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eta1 = sdpvar(length(Lambda),1);
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eta2 = sdpvar(length(Lambda),1);
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v = sdpvar(size(A,2),1);
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Model = [parametricDomainH,H*x + alpha*c0 + C*z + rhs==0,
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delta >= Lambda >= 0,
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1-delta >= b0*alpha+B*z-A*x>=0,
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sum(Lambda) >= alpha*UpperBound,
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% sum(delta)<=1,
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];
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Model = [Model, Lambda + A*v + eta2-eta1 == 0,
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0 <= eta1 <= w1, 0 <= delta - Lambda <= 1-w1,
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0 <= eta2 <= w2, 0 <= Lambda <= 1-w2];
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solvesdp(Model,-alpha)
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while double(alpha) >= 1e-5
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UpperBound = UpperBound*1.1;
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Model = [parametricDomainH,H*x + alpha*c0 + C*z + rhs==0,
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delta >= Lambda >= 0,
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1-delta >= b0*alpha+B*z-A*x>=0,
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sum(Lambda) >= alpha*UpperBound];
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Model = [Model, Lambda + A*v + eta2-eta1 == 0,
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0 <= eta1 <= w1, 0 <= delta - Lambda <= 1-w1,
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0 <= eta2 <= w2, 0 <= Lambda <= 1-w2];
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solvesdp(Model,-alpha);
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end
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dualUpper = min(U,UpperBound);
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function [c0,C] = deParameterize(c,z);
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n = length(c);
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c0C = full(getbase(c));
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c0 = c0C(:,1);
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C = c0C(:,2:end);
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if nnz(C)==0
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C = spalloc(n,length(z),0);
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else
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if length(z)>0 & size(C,2) < length(z)
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C = [];
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for i = 1:length(z)
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C = [C getbasematrix(c,getvariables(z(i)))];
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end
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end
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end
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if isempty(C)
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C = zeros(length(C),length(z));
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end
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