48 lines
1.4 KiB
Mathematica
48 lines
1.4 KiB
Mathematica
|
%%***********************************************************
|
||
|
|
%% lmiexamp1: generate SDP data for the following LMI problem
|
||
|
|
%%
|
||
|
|
%% max -eta
|
||
|
|
%% s.t. B*P + P*B' <= 0
|
||
|
|
%% -P <= -I
|
||
|
|
%% P - eta*I <= 0
|
||
|
|
%% P(1,1) = 1
|
||
|
|
%%***********************************************************
|
||
|
|
%% Here is an example on how to use this function to
|
||
|
|
%% find an optimal P.
|
||
|
|
%%
|
||
|
|
%% B = [-1 0 0; 5 -2 0; 1 1 -1];
|
||
|
|
%% [blk,At,C,b] = lmiexamp1(B);
|
||
|
|
%% [obj,X,y,Z] = sqlp(blk,At,C,b);
|
||
|
|
%% P = smat(blk(1,:),y);
|
||
|
|
%%*****************************************************************
|
||
|
|
%% SDPT3: version 4.0
|
||
|
|
%% Copyright (c) 1997 by
|
||
|
|
%% Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu
|
||
|
|
%% Last Modified: 16 Sep 2004
|
||
|
|
%%*****************************************************************
|
||
|
|
|
||
|
|
function [blk,At,C,b] = lmiexamp1(B);
|
||
|
|
|
||
|
|
n = length(B); n2 = n*(n+1)/2;
|
||
|
|
I = speye(n);
|
||
|
|
z0 = sparse(n2,1);
|
||
|
|
blktmp{1,1} = 's'; blktmp{1,2} = n;
|
||
|
|
%%
|
||
|
|
blk{1,1} = 's'; blk{1,2} = n;
|
||
|
|
blk{2,1} = 's'; blk{2,2} = n;
|
||
|
|
blk{3,1} = 's'; blk{3,2} = n;
|
||
|
|
blk{4,1} = 'u'; blk{4,2} = 1;
|
||
|
|
%%
|
||
|
|
At{1,1} = [lmifun(B,I), z0];
|
||
|
|
At{2,1} = [lmifun(-I/2,I), z0];
|
||
|
|
At{3,1} = [lmifun(I/2,I), svec(blktmp,-I,1)];
|
||
|
|
At{4,1} = sparse([1, zeros(1,n2)]);
|
||
|
|
%%
|
||
|
|
C{1,1} = sparse(n,n);
|
||
|
|
C{2,1} = -speye(n);
|
||
|
|
C{3,1} = sparse(n,n);
|
||
|
|
C{4,1} = 1;
|
||
|
|
%%
|
||
|
|
b = [zeros(n2,1); -1];
|
||
|
|
%%**********************************************************
|