79 lines
2.2 KiB
Mathematica
79 lines
2.2 KiB
Mathematica
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%%***********************************************************
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%% etp: Education testing problem.
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%%
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%% (dual problem) maximize e'*d
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%% subject to B - diag(d) >= 0
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%% d >= 0
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%%
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%% (primal problem) minimize Tr B*X
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%% subject to X >= 0
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%% diag(X) >= e
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%%
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%% Ref: M.T. Chu, J.W. Wright, IMA J. of Numerical Anal.,
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%% 15 (1995), pp. 141--160.
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%%-----------------------------------------------------------
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%% [blk,Avec,C,b,X0,y0,Z0,objval,d] = etp(B,feas,solve);
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%%
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%% B = nxn positive definite.
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%% feas = 1 if want feasible starting point
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%% = 0 if otherwise.
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%% solve = 0 just to initialize
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%% = 1 if want to solve the problem.
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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,X0,y0,Z0,objval,d] = etp(B,feas,solve);
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if (nargin < 2); feas = 0; end
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if (nargin < 3); solve = 0; end
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if isempty(feas); feas = 0; end
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if (~isreal(B))
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error('only real B allowed');
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elseif (norm(B-B','fro') > 1e-13);
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error(' B must be symmetric');
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end;
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%%
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%% validate B
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%%
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n = length(B);
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d = eig(B); d = real(d);
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if (min(d) < 0);
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error('B must be positive def');
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end;
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%%
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%%
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blk{1,1} = 's'; blk{1,2} = n;
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blk{2,1} = 'l'; blk{2,2} = n;
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b = ones(n,1);
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C{1,1} = B;
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C{2,1} = zeros(n,1);
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A = cell(2,n);
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for k = 1:n
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A{1,k} = sparse(k,k,1,n,n);
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A{2,k} = [zeros(k-1,1); -1; zeros(n-k,1)];
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end;
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Avec = svec(blk,A,ones(size(blk,1),1));
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if (feas == 1);
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y0 = 0.9*min(d)*ones(n,1);
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Z0 = ops(C,'-',Atyfun(blk,Avec,[],[],y0));
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X0{1,1} = 1.1*eye(n);
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X0{2,1} = 0.1*ones(n,1);
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elseif (feas == 0);
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[X0,y0,Z0] = infeaspt(blk,Avec,C,b);
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end;
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if (solve)
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[obj,X,y,Z] = sqlp(blk,Avec,C,b,[],X0,y0,Z0);
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objval = obj(2);
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d = y;
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else
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objval = []; d = [];
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end
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%%===========================================================
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