94 lines
2.8 KiB
Mathematica
94 lines
2.8 KiB
Mathematica
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%%*********************************************************************
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%% gdcomp: Compute gd = 1/td in Equation (15) of FOT's paper.
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%%
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%% [gd,info,blk2,At2,C2,b2] = gdcomp(blk,At,C,b,OPTIONS);
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%%
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%%*********************************************************************
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function [gd,info,blk2,At2,C2,b2] = gdcomp(blk,At,C,b,OPTIONS);
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if (nargin == 4)
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OPTIONS = sqlparameters;
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OPTIONS.vers = 1;
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OPTIONS.printlevel = 3;
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end
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if ~iscell(C); tmp = C; clear C; C{1} = tmp; end
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%%
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m = length(b);
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blk2 = blk;
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At2 = cell(size(blk,1),1);
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C2 = cell(size(blk,1),1);
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b2 = [zeros(m,1); 1; 0];
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%%
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%%
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%%
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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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if strcmp(pblk{1},'s')
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C2{p,1} = sparse(n,n);
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else
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C2{p,1} = zeros(n,1);
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end
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end
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%%
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%% New multipliers in dual problem: tt, theta.
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%% [v; tt; theta].
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%%
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ss = 0; cc = 0; aa = zeros(1,m);
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exist_ublk = 0;
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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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if strcmp(pblk{1},'s')
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At2{p} = [At{p}, svec(pblk,speye(n,n),1), -svec(pblk,C{p},1)];
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ss = ss + n;
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cc = cc + trace(C{p});
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aa = aa + svec(pblk,speye(n),1)'*At{p};
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elseif strcmp(pblk{1},'q')
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eq = zeros(n,1);
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idx1 = 1+[0,cumsum(pblk{2})];
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idx1 = idx1(1:length(idx1)-1);
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eq(idx1) = ones(length(idx1),1);
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At2{p} = [At{p}, 2*sparse(eq), -sparse(C{p})];
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ss = ss + 2*length(pblk{2});
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cc = cc + sum(C{p}(idx1));
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aa = aa + eq'*At{p};
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elseif strcmp(pblk{1},'l')
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el = ones(n,1);
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At2{p} = [At{p}, sparse(el), -sparse(C{p})];
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ss = ss + n;
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cc = cc + el'*C{p};
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aa = aa + el'*At{p};
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elseif strcmp(pblk{1},'u')
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At2{p} = [At{p}, sparse(n,1), -sparse(C{p})];
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exist_ublk = 1;
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end
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end
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%%
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%% 3 additional inequality constraints in dual problem.
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%%
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alp = max(1,sqrt(sum(abs(aa))));
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numblk = size(blk,1);
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blk2{numblk+1,1} = 'l'; blk2{numblk+1,2} = 3;
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C2{numblk+1,1} = [1; alp; 0];
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At2{numblk+1,1} = [-aa, 0, cc;
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zeros(1,m), 0, alp;
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zeros(1,m), alp, -alp];
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%%
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%% Solve SDP
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%%
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OPTIONS.gaptol = 1e-10;
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[obj,X,y,Z,info] = HSDsqlp(blk2,At2,C2,b2,OPTIONS);
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gd = 1/abs(obj(2));
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err = max([info.gap/(1+mean(abs(obj))), info.pinfeas, info.dinfeas]);
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if (OPTIONS.printlevel)
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fprintf('\n ******** gd = %3.1e, err = %3.1e\n',gd,err);
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if (err > 1e-6);
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fprintf('\n----------------------------------------------------')
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fprintf('\n gd problem is not solved to sufficient accuracy');
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fprintf('\n----------------------------------------------------\n')
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end
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end
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%%*********************************************************************
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