154 lines
6.2 KiB
Mathematica
154 lines
6.2 KiB
Mathematica
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function [Fconv,no_changed,infeasible,Forigquad] = convertquadratics(F)
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%CONVERTQUADRATICS Internal function to extract quadratic constraints
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% ******************************
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% LINEAR?
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% ******************************
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infeasible = 0;
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Fconv = F;
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no_changed = 0;
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Forigquad = [];
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if islinear(F)
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return
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end
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[monomtable,variabletype] = yalmip('monomtable');
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if any(variabletype == 4)
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if issigmonial(F)
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return
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end
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end
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Fconv = lmi;
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no_changed = 0;
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i_changed = [];
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% Make sure bounds a pre-processed, in case we look for rotated cone which
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% requires us to know lower bounds
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nv = yalmip('nvars');
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LU = yalmip('getbounds',1:nv);
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LUhere = getbounds(F,[],LU);
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for i = 1:1:length(F)
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if max(variabletype(getvariables(F(i)))) <= 1
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% Definitely no quadratic to model as all variables are bilinear at
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% most
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Fconv = Fconv + F(i);
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elseif is(F(i),'element-wise') & ~is(F(i),'linear') & ~is(F(i),'sigmonial')
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% f-c'*x-x'*Q*x>0
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fi = sdpvar(F(i));fi = fi(:);
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%[Qs,cs,fs,x,info] = vecquaddecomp(fi);
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for j = 1:length(fi)
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fij = fi(j);
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if isa(fij,'double')
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if fij < 0
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infeasible = 1;
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warning('The problem is trivially infeasible. You have a term POSITIVE NUMBER < 0.');
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return
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end
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end
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% Q = Qs{j};c = cs{j};f = fs{j};
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if max(variabletype(getvariables(fij))) <= 1
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% There are at most bilinear terms, so it cannot be convex
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info = 1;
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else
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[Q,c,f,x,info] = quaddecomp(fij);
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end
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if info==0
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if nnz(Q)==0
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% Oh, linear,...
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Fconv = Fconv + (fi(j)>=0);
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else
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% Yes, quadratic, but convex?
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% Change sign definitions
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Q = -Q;
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c = -c;
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f = -f;
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% Semi-definite case when only part of x in Q
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% Occurs, e.g, in constraints like y'*Q*y < t
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used = find(any(Q));Qred=Q(:,used);Qred = Qred(used,:);xred = x(used);
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[R,p]=chol(Qred);
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done = 0;
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if p
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% Safety check to account for low rank problems
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if all(eig(full(Qred))>=-1e-12)
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[u,s,v]=svd(full(Qred));
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r=find(diag(s)>1e-12);
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R=(u(:,r)*sqrt(s(r,r)))';
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p=0;
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else
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% Try to detect rotated SOCP (x-d)'*A*(x-d)+k<= C*y*z
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yzCandidates = find(~diag(Qred));
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if length(yzCandidates) == 2 && nnz(c(yzCandidates))==0
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%LU = yalmip('getbounds',getvariables(xred(yzCandidates)));
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LU = LUhere(getvariables(xred(yzCandidates)),:);
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if all(LU(:,1)>=0)
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yzSubQ = Qred(yzCandidates,yzCandidates);
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if yzSubQ(1,2) < 0
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C = -2*yzSubQ(1,2);
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xCandidates = setdiff(1:length(used),yzCandidates);
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A = Qred(xCandidates,xCandidates);
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[B,p]=chol(A);
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if ~p
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y = xred(yzCandidates(1));
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z = xred(yzCandidates(2));
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d = -A\(c(xCandidates)/2);
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k = f-d'*A*d;
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if abs(k)<= 1e-12
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Fconv=Fconv + lmi(rcone(B*(xred(xCandidates)-d),.5*C*y,z));
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no_changed = no_changed + 1;
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i_changed = [i_changed i];
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done = 1;
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elseif k >= -1e-12
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Fconv=Fconv + lmi(rcone([B*(xred(xCandidates)-d);sqrt(abs(k))],.5*C*y,z));
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no_changed = no_changed + 1;
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i_changed = [i_changed i];
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done = 1;
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else
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p = 1;
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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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end
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end
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if p==0 && ~done
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% Write as second order cone
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d = -c'*x-f;
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if isa(d,'double')
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if d<0
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infeasible = 1;
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return
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else
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Fconv=Fconv + lmi(cone([R*xred],sqrt(d)));
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end
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else
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if length(c) == length(xred)
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ctilde = -(R')\(c/2);
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Fconv=Fconv + lmi(cone([R*xred;.5*(1-d)],.5*(1+d)));
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else
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Fconv=Fconv + lmi(cone([R*xred;.5*(1-d)],.5*(1+d)));
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end
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end
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no_changed = no_changed + 1;
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i_changed = [i_changed i];
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elseif ~done
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Fconv = Fconv + lmi(fi(j));
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end
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end
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else
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Fconv = Fconv + lmi(fi(j));
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end
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end
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else
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Fconv = Fconv + F(i);
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end
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end
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if ~isempty(i_changed)
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Forigquad = F(i_changed);
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else
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Fconv = F;
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end
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