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From: "Johan L?fberg" <loefberg@control.ee.ethz.ch>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Equality constraints in LMI..elementwise implementation....reproduction of neural network in Park& Park paper
Date: Tue, 25 Aug 2009 16:56:03 +0000 (UTC)
Organization: ETH Zurich
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To begin with, the equations don't make sense, the left multiplication using alpha_i^k should be transposed.

Assuming that is the case, I don't see why LMIs and SDP should be involved here. There are no semidefinite stuff involved in the original equation (7). (unless there is an implicit SDP constraint on T that I am missing)

The problem is trivial to implement in, e.g., the MATLAB toolbox YALMIP, solvable using bisection on an LP, or by simply using the global solver in YALMIP. email me if you need help.


"Varsha Bhambhani" <bhambhani.v@gmail.com> wrote in message <h6mscc$pgc$1@fred.mathworks.com>...
> Uses LMI toolbox in matlab to implement problem defined by Park & Park  (paper attached).however problem results in infeasibility....
> 
> Implementing eq 9 and 10 in park & park paper "An optimization approach to design of cellular neural networks"International Journal of Systems Science, 2000, volume 31, number 12, pages 1585 ? 1591
> 
> two problems encountered...
> 1) y is the problem infeasible in my code whereas feasible results are obtained in aprk & park using GEVP
> 
> 2) where to use equality constraints to define Tii=0 and T=T'=T|S elementwise as in park & park
> 
> I think the structure of my LMI equations using lmivar and lmiterm is correct
> 
> The code is as such....
> 
> 
> 
> clear all;
> clc;
> A1=[1 1 1 1 -1 -1 1 -1 -1 1 1 1]';
> A2=[1 -1 1 1 1 1 1 -1 1 1 -1 1]';
> A3=[1 1 1 1 -1 1 1 1 1 1 -1 -1]';
> A4=[-1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1]';
> S= [1 1 0 1 1 0 0 0 0 0 0 0; 1 1 1 1 1 1 0 0 0 0 0 0; 0 1 1 0 1 1 0 0 0 0 0 0; 1 1 0 1 1 0 1 1 0 0 0 0; 1 1 1 1 1 1 1 1 1 0 0 0; 0 1 1 0 1 1 0 1 1 0 0 0; 0 0 0 1 1 0 1 1 0 1 1 0; 0 0 0 1 1 1 1 1 1 1 1 1; 0 0 0 0 1 1 0 1 1 0 1 1; 0 0 0 0 0 0 1 1 0 1 1 0; 0 0 0 0 0 0 1 1 1 1 1 1; 0 0 0 0 0 0 0 1 1 0 1 1];
> L=1;
> U=10;
> I= eye(12);
> W=ones(12,12);
> setlmis([])
> T = lmivar(1,[12 1]);
> B = lmivar(2,[12 1]);
> P = lmivar(1,[12 0]);
> Q = lmivar(1,[12 0]);
> 
> 
> 
> 
> lmiterm([-1 1 1 T],1,A1*A1'*I);
> lmiterm([-1 1 1 B],1,A1'*I);
> lmiterm([-1 1 1 P],-1,1);
> 
> lmiterm([-2 1 1 T],1,A2*A2'*I);
> lmiterm([-2 1 1 B],1,A2'*I);
> lmiterm([-2 1 1 P],-1,1);
> 
> lmiterm([-3 1 1 T],1,A3*A3'*I);
> lmiterm([-3 1 1 B],1,A3'*I);
> lmiterm([-3 1 1 P],-1,1);
> 
> lmiterm([-4 1 1 T],1,A4*A4'*I);
> lmiterm([-4 1 1 B],1,A4'*I);
> lmiterm([-4 1 1 P],-1,1);
> 
> 
> lmiterm([-5 1 1 Q],1,W);
> lmiterm([-5 1 1 T],1,-1);
> 
> lmiterm([-6 1 1 Q],1,W);
> lmiterm([-6 1 1 T],1,1);
> 
> lmiterm([-7 1 1 Q],1,1);
> lmiterm([7 1 1 0],L*I);
> 
> lmiterm([-8 1 1 0],U*I);
> lmiterm([8 1 1 Q],1,I);
> 
> lmiterm([-9 1 1 Q],2,1);
> lmiterm([9 1 1 P],-1,1);
> 
> % lmiterm([-10 1 1 -T],1/2,-1,'s');
> % lmiterm([-10 1 1 T],1,1);
> % 
> % lmiterm([11 1 1 -T],1/2,-1,'s');
> % lmiterm([11 1 1 T],1,1);
> % [m,n]=size(S);
> % for i=1:m
> %     for j =1:n
> %     if S(i,j)==1
> %         T(i,j)=T(i,j);
> %     else
> %         T(i,j)=0;
> %     end
> %     if (i==j)
> %         T(i,j)=0;
> %     else
> %         T(i,j)=T(i,j);
> %     end
> %     end
> % end
> test_LMIs = getlmis;
> [alpha,Qopt]=gevp(test_LMIs,9)