115 lines
4.0 KiB
Mathematica
115 lines
4.0 KiB
Mathematica
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% *************************************************************************
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% Tighten bounds at root
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% *************************************************************************
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function p = root_node_tighten(p,upper);
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p.feasible = all(p.lb<=p.ub) & p.feasible;
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if p.options.bmibnb.roottight & p.feasible
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pin = p;
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if ~isempty(p.bilinears)
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% f = p.F_struc(1:p.K.f,:);
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% p.F_struc(1:p.K.f,:)=[];
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% p = addBilinearVariableCuts(p);
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% p.F_struc = [f;p.F_struc];
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% % p.K.l = 0;
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end
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if ~isempty(p.bilinears) && ~isinf(upper)
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p_cut = p;
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for i = 1:size(p.bilinears,1)
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if p_cut.c(p.bilinears(i,1))
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p_cut.Q(p.bilinears(i,2),p.bilinears(i,3)) = p_cut.c(p.bilinears(i,1))/2;
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p_cut.Q(p.bilinears(i,3),p.bilinears(i,2)) = p_cut.Q(p.bilinears(i,3),p.bilinears(i,2))+p_cut.c(p.bilinears(i,1))/2;
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p_cut.c(p.bilinears(i,1)) = 0;
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end
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end
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if all(eig(p_cut.Q)>=0)
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[u,s,v] = svd(full(p_cut.Q));
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% f + c'*x + x'*Q*x <= U
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% c'*x + x'*R*R*x <= U - f - c'*x
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% ||Rx||^2 <= upperbound U - f - c'*x
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% ||Rx||_inf <= n*sqrt(upperbound U - f - c'*x)
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rhs = upper - p.f;
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neg = find(p_cut.c<0);
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pos = find(p_cut.c>0);
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rhs = rhs - sum(p.ub(neg).*p_cut.c(neg));
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rhs = rhs - sum(p.lb(pos).*p_cut.c(pos));
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if rhs > 0
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R = diag(diag(s).^.5)*v';
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R = R(diag(s)>1e-10,:);
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% -n*sqrt(rhs) <= R*x <= n*sqrt(R)
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p.F_struc = [p.F_struc;size(v,2)*sqrt(rhs)*ones(size(R,1),1) -R;size(v,2)*sqrt(rhs)*ones(size(R,1),1) R];
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p.K.l = p.K.l + 2*size(R,1);
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end
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end
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end
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if all(p.K.q == 0) & all(p.K.s == 0) & all(p.K.r == 0)
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lowersolver = eval(['@' p.solver.lpcall]);
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else
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lowersolver = eval(['@' p.solver.lowercall]);
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end
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c = p.c;
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Q = p.Q;
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mt = p.monomtable;
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p.monomtable = eye(length(c));
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i = 1;
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% Add an upper bound cut?
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if (upper < inf)
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% p.c'*x+p.f < upper
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newline = [upper-p.f -p.c'];
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p.F_struc = [p.F_struc(1:p.K.f,:);newline;p.F_struc(1+p.K.f:end,:)];
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p.K.l = p.K.l + 1;
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end
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while i<=length(p.linears) & p.feasible
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j = p.linears(i);
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if p.lb(j) < p.ub(j) & (ismember(j,p.branch_variables) | (p.options.bmibnb.roottight == 2))
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p.c = eyev(length(p.c),j);
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output = feval(lowersolver,removenonlinearity(p));
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p.counter.lowersolved = p.counter.lowersolved + 1;
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if (output.problem == 0) & (output.Primal(j)>p.lb(j)+1e-4)
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p.lb(j) = output.Primal(j);
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p = updateonenonlinearbound(p,j);
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p = clean_bounds(p);
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end
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if output.problem == 1
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p.feasible = 0;
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elseif p.lb(j) < p.ub(j) % We might have updated lb
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p.c = -eyev(length(p.c),j);
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output = feval(lowersolver,removenonlinearity(p));
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p.counter.lowersolved = p.counter.lowersolved + 1;
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if (output.problem == 0) & (output.Primal(j) < p.ub(j)-1e-4)
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p.ub(j) = output.Primal(j);
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if p.ub(j)<p.lb(j)
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p.ub(j) = p.lb(j);
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end
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p = updateonenonlinearbound(p,j);
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p = clean_bounds(p);
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end
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if output.problem == 1
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p.feasible = 0;
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end
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i = i+1;
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end
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else
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i = i + 1;
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end
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end
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% if upper < inf
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% p.F_struc(1+p.K.f,:) = [];
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% p.K.l = p.K.l - 1;
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% end
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%
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% p.c = c;
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% p.Q = Q;
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% p.monomtable = mt;
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p.lb(p.lb<-1e10) = -inf;
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p.ub(p.ub>1e10) = inf;
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pin.lb = p.lb;
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pin.ub = p.ub;
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pin.feasible = p.feasible;
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pin.counter = p.counter;
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p = pin;
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end
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