241 lines
9.9 KiB
Mathematica
241 lines
9.9 KiB
Mathematica
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function [output,cost,psave,timing] = solvelower(p,options,lowersolver,xmin,upper,timing)
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psave = p;
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removeThese = find(p.InequalityConstraintState==inf);
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p.F_struc(p.K.f + removeThese,:) = [];
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p.K.l = p.K.l - length(removeThese);
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removeThese = find(p.EqualityConstraintState==inf);
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p.F_struc(removeThese,:) = [];
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p.K.f = p.K.f - length(removeThese);
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if p.options.bmibnb.cut.bilinear
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p_cut = addBilinearVariableCuts(p);
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end
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if p.options.bmibnb.cut.evalvariable
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p_cut = addEvalVariableCuts(p_cut);
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psave.evalMap = p_cut.evalMap;
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end
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if p.options.bmibnb.cut.monomial
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p_cut = addMonomialCuts(p_cut);
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end
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if p.options.bmibnb.cut.multipliedequality
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p_cut = addMultipliedEqualityCuts(p_cut);
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end
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if p.options.bmibnb.cut.convexity
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p_cut = addConvexityCuts(p_cut);
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end
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if p.options.bmibnb.cut.complementarity
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p_cut = addComplementarityCuts(p_cut);
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end
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% **************************************
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% SOLVE NODE PROBLEM
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% **************************************
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if any(p_cut.ub+1e-8<p_cut.lb)
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output.problem=1;
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cost = inf;
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else
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% We are solving relaxed problem (penbmi might be local solver)
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p_cut.monomtable = eye(length(p_cut.c));
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if p.solver.lowersolver.objective.quadratic.convex
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% Setup quadratic
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[p_cut.Q,p_cut.c] = compileQuadratic(p.c,p);
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if nonconvexQuadratic(p_cut.Q);
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p_cut.Q = p.Q;
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p_cut.c = p.c;
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end
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end
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fixed = p_cut.lb >= p_cut.ub;
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if nnz(fixed) == length(p.c)
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% All variables are fixed to a bound
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output.Primal = p.lb;
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res = constraint_residuals(p,output.Primal);
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eq_ok = all(res(1:p.K.f)>=-p.options.bmibnb.eqtol);
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iq_ok = all(res(1+p.K.f:end)>=p.options.bmibnb.pdtol);
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feasible = eq_ok & iq_ok;
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if feasible
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output.problem = 0;
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else
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output.problem = 1;
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end
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cost = output.Primal'*p.Q*output.Primal + p.c'*output.Primal + p.f;
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else
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if nnz(fixed)==0
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if ~isempty(p_cut.bilinears) & 0
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top = size(p_cut.F_struc,1);
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if length(p_cut.K.s)==1 & p_cut.K.s(1)==0
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p_cut.K.s = [];
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end
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usedterms = zeros(size(p_cut.bilinears,1),1);
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for i = 1:size(p_cut.bilinears,1)
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if ~usedterms(i)
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windex = p_cut.bilinears(i,1);
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xindex = p_cut.bilinears(i,2);
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yindex = p_cut.bilinears(i,3);
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if xindex ~=yindex
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% OK, we have a bilinear term
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xsquaredindex = find(p_cut.bilinears(:,2)==xindex & p_cut.bilinears(:,3)==xindex);
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ysquaredindex = find(p_cut.bilinears(:,2)==yindex & p_cut.bilinears(:,3)==yindex);
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if ~isempty(xsquaredindex) & ~isempty(ysquaredindex)
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usedterms(i) = 1;
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usedterms(xsquaredindex) = 1;
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usedterms(ysquaredindex) = 1;
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xsquaredindex = p_cut.bilinears(xsquaredindex,1);
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ysquaredindex = p_cut.bilinears(ysquaredindex,1);
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if 0
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Z = zeros(9,size(p_cut.F_struc,2));
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Z(1,xsquaredindex+1) = 1;
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Z(2,windex+1) = 1;
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Z(4,windex+1) = 1;
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Z(5,ysquaredindex+1) = 1;
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Z(3,xindex+1) = 1;
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Z(7,xindex+1) = 1;
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Z(6,yindex+1) = 1;
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Z(8,yindex+1) = 1;
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Z(9,1)=1;
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else
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xL = p.lb(xindex);
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yL = p.lb(yindex);
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Z = zeros(9,size(p_cut.F_struc,2));
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Z(1,xsquaredindex+1) = 1;
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Z(2,windex+1) = 1;
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Z(4,windex+1) = 1;
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Z(5,ysquaredindex+1) = 1;
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Z(3,xindex+1) = 1;
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Z(7,xindex+1) = 1;
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Z(6,yindex+1) = 1;
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Z(8,yindex+1) = 1;
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Z(9,1)=1;
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Z(3,1) = -xL;
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Z(7,1) = -xL;
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Z(6,1) = -yL;
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Z(8,1) = -yL;
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Z(1,xindex+1) = -2*xL;
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Z(5,yindex+1) = -2*yL;
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Z(1,1) = xL^2;
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Z(5,1) = yL^2;
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Z(4,xindex+1) = -yL;
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Z(4,yindex+1) = -xL;
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Z(4,1) = xL*yL;
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Z(2,xindex+1) = -yL;
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Z(2,yindex+1) = -xL;
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Z(2,1) = xL*yL;
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end
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p_cut.F_struc = [p_cut.F_struc;Z];
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p_cut.K.s = [p_cut.K.s 3];
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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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p_cut.linearindicies = 1:length(p.c);
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p_cut.nonlinearindicies = [];
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p_cut.variabletype = zeros(1,length(p.c));
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p_cut.deppattern = eye(length(p.c));
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p_cut.linears = 1:length(p.c);
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p_cut.bilinears = [];
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p_cut.nonlinears = [];
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p_cut.monomials = [];
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p_cut.evaluation_scheme = [];
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tstart = tic;
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output = feval(lowersolver,removenonlinearity(p_cut));
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psave.counter.lowersolved = psave.counter.lowersolved + 1;
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timing.lowersolve = timing.lowersolve + toc(tstart);
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cost = output.Primal'*p_cut.Q*output.Primal + p_cut.c'*output.Primal + p.f;
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% Minor clean-up
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pp=p;
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output.Primal(output.Primal<p.lb) = p.lb(output.Primal<p.lb);
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output.Primal(output.Primal>p.ub) = p.ub(output.Primal>p.ub);
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x=output.Primal;
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return
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else
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pp = p_cut;
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removethese = fixed;
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if ~isempty(p_cut.F_struc)
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p_cut.F_struc(:,1)=p_cut.F_struc(:,1)+p_cut.F_struc(:,1+find(fixed))*p_cut.lb(fixed);
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p_cut.F_struc(:,1+find(fixed))=[];
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rf = find(~any(p_cut.F_struc,2));
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rf = rf(rf<=(p_cut.K.f + p_cut.K.l));
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p_cut.F_struc(rf,:) = [];
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p_cut.K.l = p_cut.K.l - nnz(rf>p_cut.K.f);
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p_cut.K.f = p_cut.K.f - nnz(rf<=p_cut.K.f);
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end
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p_cut.c(removethese)=[];
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if nnz(p_cut.Q)>0
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p_cut.c = p_cut.c + 2*p_cut.Q(find(~removethese),find(removethese))*p_cut.lb(removethese);
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p_cut.Q(:,find(removethese))=[];
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p_cut.Q(find(removethese),:)=[];
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else
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p_cut.Q = spalloc(length(p_cut.c),length(p_cut.c),0);
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end
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if ~isempty(p_cut.binary_variables)
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new_bin = [];
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new_var = find(~fixed);
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for i = 1:length(p_cut.binary_variables)
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temp = find(p_cut.binary_variables(i) == new_var);
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new_bin = [new_bin temp(:)'];
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end
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p_cut.binary_variables = new_bin;
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end
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if ~isempty(p_cut.integer_variables)
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new_bin = [];
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new_var = find(~fixed);
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for i = 1:length(p_cut.integer_variables)
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temp = find(p_cut.integer_variables(i) == new_var);
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new_bin = [new_bin temp(:)'];
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end
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p_cut.integer_variables = new_bin;
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end
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p_cut.lb(removethese)=[];
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p_cut.ub(removethese)=[];
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p_cut.x0(removethese)=[];
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p_cut.monomtable(:,find(removethese))=[];
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p_cut.monomtable(find(removethese),:)=[];
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% The model can become absolutely trivial in some case
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% For instance in ex9_2_2 everything is presolved
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if nnz(p_cut.c)==0 & nnz(p_cut.Q)==0 & size(p_cut.F_struc,1)==0
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% No objective and no constraints
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if all(p_cut.lb <= p_cut.ub)
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output.Primal = (p_cut.lb + p_cut.ub)/2;
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output.Primal(isinf(p_cut.lb) & isinf(p_cut.ub))=0;
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output.problem = 0;
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else
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output.Primal = zeros(length(p_cut.lb),1);
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output.problem = 1;
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end
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else
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try
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tstart = tic;
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output = feval(lowersolver,removenonlinearity(p_cut));
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psave.counter.lowersolved = psave.counter.lowersolved + 1;
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timing.lowersolve = timing.lowersolve + toc(tstart);
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catch
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1
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end
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end
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x=full(p.c*0);
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x(removethese)=p.lb(removethese);
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x(~removethese)=output.Primal;
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output.Primal = x;
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cost = output.Primal'*pp.Q*output.Primal + pp.c'*output.Primal + p.f;
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end
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end
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end
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