62 lines
1.8 KiB
Mathematica
62 lines
1.8 KiB
Mathematica
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%%***********************************************************
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%% lmiexamp2: generate SDP data for the following LMI problem
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%%
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%% max -Tr(P)
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%% s.t. A1*P + P*A1' + B*diag(d)*B' <= 0
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%% A2*P + P*A2' + B*diag(d)*B' <= 0
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%% -d <= 0
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%% sum(d) = 1
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%%***********************************************************
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%% Here is an example on how to use this function to
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%% find an optimal P.
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%%
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%% A1 = [-1 0 0; 0 -2 0; 1 1 -1];
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%% A2 = A1 + 0.1*A1';
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%% B = [1 2; 3 4; 5 6];
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%%
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%% [blk,Avec,C,b] = lmiexamp2(A1,A2,B);
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%% [obj,X,y,Z] = sqlp(blk,Avec,C,b);
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%% n = size(A1,2); N = n*(n+1)/2; dlen = size(B,2);
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%% P = smat(blk(1,:),y(1:N));
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%% d = y(N+[1:dlen]);
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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 [blk,Avec,C,b] = lmiexamp2(A1,A2,B);
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%%
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n1 = size(A1,2); n2 = size(A2,2);
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if (n1 ~= n2); error('lmiexamp2: A1, A2 not compatible'); end;
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%%
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n = n1;
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I = speye(n);
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blk{1,1} = 's'; blk{1,2} = n;
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Avec{1,1} = lmifun(A1,I,B);
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C{1,1} = sparse(n,n);
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%%
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blk{2,1} = 's'; blk{2,2} = n;
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Avec{2,1} = lmifun(A2,I,B);
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C{2,1} = sparse(n,n);
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%%
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%% and constraints: -d <= 0
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%%
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N = n*(n+1)/2; dlen = size(B,2);
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blk{3,1} = 'l'; blk{3,2} = dlen;
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Avec{3,1} = [sparse(dlen,N) -speye(dlen,dlen)];
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C{3,1} = zeros(dlen,1);
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%%
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%% add in the constraint: sum(d) = 1
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%%
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blk{4,1} = 'u'; blk{4,2} = 1;
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Avec{4,1} = sparse([zeros(1,N) ones(1,dlen)]);
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C{4,1} = 1;
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%%
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blktmp{1,1} = 's'; blktmp{1,2} = n;
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b = [-svec(blktmp,I); zeros(dlen,1)];
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%%**********************************************************
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