144 lines
5.9 KiB
Mathematica
144 lines
5.9 KiB
Mathematica
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function pout = propagatequadratics(p)
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pout = p;
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if p.bilinears~=0
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F_struc = p.F_struc;
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p.F_struc = [-p.F_struc(1:p.K.f,:);p.F_struc];
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p.K.f=2*p.K.f;
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InequalityConstraintState = [p.EqualityConstraintState;p.EqualityConstraintState;p.InequalityConstraintState];
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if p.K.l+p.K.f>0
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quadratic_variables = find(p.bilinears(:,2) == p.bilinears(:,3));
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if ~isempty(quadratic_variables)
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quadratic_variables = p.bilinears(quadratic_variables,1);
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for i = 1:length(quadratic_variables)
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k = quadratic_variables(i);
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if (p.lb(k) < p.ub(k)-1e-4)
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x = p.bilinears(p.bilinears(:,1)==k,2);% x^2
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candidates = find((InequalityConstraintState==1) & p.F_struc(1:p.K.f+p.K.l,1+k))';
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for j = candidates
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a = p.F_struc(j,2:end);
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b = p.F_struc(j,1);
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aij = a(k);
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% rest + cij*x + (+-)x^2 >= 0
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cij = a(x);
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cij = cij/abs(aij);
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b = b/abs(aij);
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a = a/abs(aij);
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% aij = sign(aij);
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a(k) = 0;
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a(x) = 0;
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indNEG = find(a < 0);
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indPOS = find(a > 0);
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LB = p.lb;
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UB = p.ub;
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LB(k) = 0;
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UB(k) = 0;
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LB(x) = 0;
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UB(x) = 0;
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a(k) = 0;
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a(x) = 0;
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if aij < 0
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% rest + cij*x - x^2 >= 0
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% Derive upper bound on rest
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rest = (b+a([indPOS(:);indNEG(:)])*[UB(indPOS);LB(indNEG)]);
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% Write as rest >= (x - center)^2-(center)^2
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center = cij/2;
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radii2 = rest + (cij/2)^2;
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newUB = center + sqrt(radii2);
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newLB = center - sqrt(radii2);
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p.lb(x) = max(p.lb(x),newLB);
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p.ub(x) = min(p.ub(x),newUB);
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else
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% rest + cij*x + x^2 >= 0
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% (x+cij/2)^2 - (cij/2)^2 + rest >= 0
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% (x+cij/2)^2 >= radii
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% Lower bound on rest
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rest = (b+a([indPOS(:);indNEG(:)])*[UB(indPOS);LB(indNEG)]);
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center = -cij/2;
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radii2 = -rest + (cij/2)^2;
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if radii2 > 0
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left = center-sqrt(radii2);
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right = center+sqrt(radii2);
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if p.ub(x) < right
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p.ub(x) = min(p.ub(x),left);
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end
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if p.lb(x) > left
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p.lb(x) = max(p.lb(x),right);
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end
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end
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end
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end
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elseif p.lb(k)<0
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end
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end
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end
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end
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if p.K.l+p.K.f>0
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bilinear_variables = find(p.bilinears(:,2) ~= p.bilinears(:,3));
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if ~isempty(bilinear_variables)
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bilinear_variables = p.bilinears(bilinear_variables,1);
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for i = 1:length(bilinear_variables)
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k = bilinear_variables(i);
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if p.lb(k) >= -5000000000 & (p.lb(k) < p.ub(k)-1e-4)
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x = p.bilinears(p.bilinears(:,1)==k,2);% x^2
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y = p.bilinears(p.bilinears(:,1)==k,3);% x^2
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candidates = find((InequalityConstraintState==1) & p.F_struc(1:p.K.f+p.K.l,1+k))';
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for j = candidates
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a = p.F_struc(j,2:end);
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aij = a(k);
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if aij > 0
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indNEG = find(a < 0);
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indPOS = find(a > 0);
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LB = p.lb;
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UB = p.ub;
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LB(k) = 0;
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UB(k) = 0;
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a(k) = 0;
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newLB = (-p.F_struc(j,1)-a([indPOS(:);indNEG(:)])*[UB(indPOS);LB(indNEG)])/aij;
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p.lb(k) = max(p.lb(k),newLB);
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elseif aij < 0
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indNEG = find(a < 0);
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indPOS = find(a > 0);
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LB = p.lb;
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UB = p.ub;
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LB(k) = 0;
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UB(k) = 0;
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a(k) = 0;
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newUB = (p.F_struc(j,1)+a([indPOS(:);indNEG(:)])*[UB(indPOS);LB(indNEG)])/(-aij);
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p.ub(k) = min(p.ub(k),newUB);
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end
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end
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if p.lb(k)>0 & p.lb(x)>0 & p.lb(y)>0
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p.ub(x) = min(p.ub(x), p.ub(k)/p.lb(y));
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p.ub(y) = min(p.ub(y), p.ub(k)/p.lb(x));
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p.lb(x) = max(p.lb(x), p.lb(k)/p.ub(y));
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p.lb(y) = max(p.lb(y), p.lb(k)/p.ub(x));
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end
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elseif p.lb(k)<0
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end
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end
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end
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end
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end
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if ~isequal([p.lb p.ub],[pout.lb pout.ub])
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pout.changedbounds = 1;
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end
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pout.lb = p.lb;
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pout.ub = p.ub;
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