75 lines
2.1 KiB
Mathematica
75 lines
2.1 KiB
Mathematica
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%%*****************************************************************
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%% compute lower and upper bounds for the exact primal
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%% optimal value.
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%%
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%% LB <= true optimal dual value = true optimal primal value <= UB.
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%%
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%%*****************************************************************
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%% SDPT3: version 4.0
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%% Copyright (c) 1997 by
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%% Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu
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%% Last Modified: 16 Sep 2004
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%%*****************************************************************
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function [LB,UB] = SDPvalBounds(blk,At,C,b,X,y,mu);
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if (nargin < 7); mu = 1.1; end
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Aty = Atyfun(blk,At,[],[],y);
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Znew = ops(C,'-',Aty);
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%%
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eigX = cell(size(blk,1),1);
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for p = 1:size(blk,1)
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pblk = blk(p,:);
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if strcmp(pblk{1},'s')
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eigX{p} = eig(full(X{p}));
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elseif strcmp(pblk{1},'l')
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eigX{p} = X{p};
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end
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end
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%%
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%% compute lower bound
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%%
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pert = 0;
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for p = 1:size(blk,1)
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pblk = blk(p,:);
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if strcmp(pblk{1},'s')
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eigtmp = eig(full(Znew{p}));
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idx = find(eigtmp < 0);
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Xbar = mu*max(eigX{p});
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elseif strcmp(pblk{1},'l')
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eigtmp = Znew{p};
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idx = find(eigtmp < 0);
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Xbar = mu*max(eigX{p});
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end
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numneg = length(idx);
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if (numneg)
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mineig = min(eigtmp(idx));
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pert = pert + Xbar*sum(eigtmp(idx));
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%%fprintf('\n numneg = %3.0d, mineigZnew = %- 3.2e',numneg,mineig);
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end
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end
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LB0 = b'*y;
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LB = b'*y + pert;
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fprintf('\n <b,y> = %-10.9e, LB = %-10.9e\n',LB0,LB);
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%%
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%% compute upper bound
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%%
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Xbar = X;
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%% construct Xbar that is positive semidefinite
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for p = 1:size(blk,1)
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pblk = blk(p,:);
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n = sum(pblk{2});
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eigXp = eigX{p};
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if strcmp(pblk{1},'s')
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Xbar{p} = Xbar{p} - min(eigXp)*speye(n,n);
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elseif strcmp(pblk{1},'l')
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Xbar{p} = Xbar{p} - min(eigXp)*ones(n,1);
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end
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end
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Rp = b-AXfun(blk,At,[],Xbar);
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UB = blktrace(blk,C,Xbar) + mu*abs(y)'*abs(Rp);
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UB0 = blktrace(blk,C,X);
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fprintf('\n <C,X> = %-10.9e, UB = %-10.9e\n',UB0,UB);
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%%*****************************************************************
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