94 lines
3.7 KiB
Mathematica
94 lines
3.7 KiB
Mathematica
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function p = addImpliedSDP(p)
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if p.K.q(1)==0 && p.K.s(1) > 0
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% Search for rows where there is a constant, and a diagonal term
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% which thus has to be structly positive, we might leads us to a
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% constraints of the type sum x_i >= 1, if only non-negative integer
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% variables are involved, entering with positive coefficient (and v.s)
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newF = [];
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top = p.K.f + p.K.l + 1;
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for i = 1:length(p.K.s)
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F = p.F_struc(top:top + p.K.s(i)^2-1,:);
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X0 = reshape(F(:,1),p.K.s(i),p.K.s(i));
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candidates = find(any(X0-diag(diag(X0)),2) & (diag(X0)<=0));
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if ~isempty(candidates);
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I = speye(p.K.s(i),p.K.s(i));
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pos = find(I(:));
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for j = candidates(1:end)'
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row = F(pos(j),2:end);
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used = find(row);
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if ~isempty(used)
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if ~any(row(p.noninteger_variables))
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if all(row <=0) && all(p.ub(used)<=0)
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row(find(row)) = 1;
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newF = [newF;-1 -row];
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elseif all(row >=0) && all(p.lb(used)>=0)
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row(find(row)) = 1;
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newF = [newF;-1 row];
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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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top = top + p.K.s(i)^2;
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end
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if size(newF,1)>0
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p.F_struc = [p.F_struc(1:p.K.f + p.K.l,:);
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newF;
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p.F_struc(1+p.K.f+p.K.l:end,:)];
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p.K.l = p.K.l + size(newF,1);
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end
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% Search for trivial variables entering in diagonal elements alone, and
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% not entering anywhere else in model. Bad modelling?
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% First, they should not appear in LP cone (can be generalized by
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% checking that it acts in the correct direction)
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% TODO: Check for possibility of different signs etc, currently only
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% implemented for typical test cases
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candidates = find(~any(p.F_struc(1:p.K.f + p.K.l,2:end),1));
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fixable = nan(1,length(candidates));
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top = p.K.f + p.K.l + 1;
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for j = 1:length(p.K.s)
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F = p.F_struc(top:top + p.K.s(j)^2-1,:);
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for i = 1:length(candidates(:)')
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X0 = reshape(F(:,1 + candidates(i)),p.K.s(j),p.K.s(j));
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% Diagonal matrix?
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d = diag(X0);
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if nnz((X0-diag(d)))==0
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if all(sign(d)<=0) && p.c(i)>=0 && (isnan(fixable(i)) || fixable(i)==-1)
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fixable(i) = -1;
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elseif all(sign(d)>=0) && p.c(i)<=0 && (isnan(fixable(i)) || fixable(i)==1)
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fixable(i) = 1;
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else
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fixable(i) = 0;
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end
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else
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fixable(i) = 0;
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end
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end
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top = top + p.K.s(j)^2;
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end
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p.adjustable = candidates(find(fixable));
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for i = candidates(find(~isnan(fixable)))
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% if fixable(i) == -1
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% if ~isinf(p.lb(i))
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% % p.ub(i) = p.lb(i);
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% % p.F_struc(:,1) = p.F_struc(:,1) + p.F_struc(:,i+1)*p.lb(i);
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% % p.F_struc(:,i+1) = 0;
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% % else
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% % % TODO whole row/column should be removed from the LMI!
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% end
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% elseif fixable(i) == 1
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% if ~isinf(p.ub(i))
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% % p.ub(i) = p.lb(i);
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% % p.F_struc(:,1) = p.F_struc(:,1) + p.F_struc(:,i+1)*p.lb(i);
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% % p.F_struc(:,i+1) = 0;
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% % else
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% % % TODO whole row/column should be removed from the LMI!
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% end
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% end
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end
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end
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