Talk:Beginning with CVX

From Wikimization

lamda_W=eig(full(W))

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Thanks a lot for all the ideas, they all are greats.

I think I'm wrong with this code, I would like to put the if - else - end with the another constraits, inside the cxv_begin, but the CVX don't let me doing it. Some ideas?

I come work thinking on you idea. I think you idea it’s right and I’m making thinks wrong.

I have a dude.

The new code could be:

1º I calculate some variables,

2º with one if (with depends to variables point 1º) I select one linear constrint depending value of variables in 1º and I make all the: minimize…subjet to with apropiate constraints, convex and the one linear,

if

  cvx_begin
  ...
  cvx_end

else

  cvx_begin
  ...
  cvx_end

end

3ºIf there is not solution STOP, if there is, go to 1º,

I’ve tried making this, I make: 1º, 2, 3º; return to 1º,2º, 3º And here the CVX says that there is not solution, that’s the reason for trying to keep inside the if – else.

My dude is, why CVX says there is not solution, it could be because the iteration (making steps 1-2-3) before is the correct. For explain (I know my English isn’t the best, and it’s hard for me to explain and for you to read)

         One iteracion (steps 1, 2, 3)

         All well

         Save data = DATA1

         One iteracion (steps 1, 2, 3)

         All well

         Save data = DATA2

         One iteracion (steps 1, 2, 3)

         Wrong, no solution

         Correct data = DATA2

What do you think? Any idea?

Thanks a lot for all.

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I don't know how to initialice Epsilon1 and Epsilon2. I'm trying different values.

Thanks a lot again.

Here is the new code:

%0)Initialization
clear all;
n=2; m=1;

A_a=3*eye(2*n,2*n)
B_a=4*eye(2*n,2*m) 

%1)1
W=eye(4)
R=(zeros(2,4))

%2)2
H=W*A_a'+A_a*W-B_a*R-R'*B_a'

lamda_W=min(eig(full(W)))
lamda_H=max(eig(H))

Epsilon1=11;
Epsilon2=0.1;

if(lamda_W>=Epsilon1)
    if(lamda_H<=-Epsilon2)     para=1
    else para = 0
    end
else para =0
end

%while para==0
    %3)3
    [v_W,D] = eig( full ( W ) )
    [v_H,D] = eig( full ( H ) )
    
 %   v_W_1 = v_W( : , 1 ) / norm ( v_W ( : , 1 ) ) ;
 %   v_W_2 = v_W( : , 2 ) / norm ( v_W ( : , 2 ) ) ;
 %   v_W_3 = v_W( : , 3 ) / norm ( v_W ( : , 3 ) ) ;
 %   v_W_4 = v_W( : , 4 ) / norm ( v_W ( : , 4 ) ) ;
    
 %   v_H_1 = v_H( : , 1 ) / norm ( v_H ( : , 1 ) ) ;
 %   v_H_2 = v_H( : , 2 ) / norm ( v_H ( : , 2 ) ) ;
 %   v_H_3 = v_H( : , 3 ) / norm ( v_H ( : , 3 ) ) ;
 %   v_H_4 = v_H( : , 4 ) / norm ( v_H ( : , 4 ) ) ;

    %4a)4a
if ( Epsilon1 - lamda_W )>(lamda_H+Epsilon2)
    Caso=1 %For know where am I

    cvx_begin
    variables p1 p2 W(4,4) R(2,4)
    
    minimize (p1+p2)
    
    subject to

        W(1,1)<=p1
        W(2,2)<=p1
        W(1,1)>=Epsilon1
        W(2,2)>=Epsilon1
        W(3,3)==W(1,1)
        W(4,4)==W(2,2)

        R(1,1)>=-p2
        R(1,1)<=p2
        R(2,3)==R(1,1)
        R(1,2)>=-p2
        R(1,2)<=p2
        R(2,4)==R(1,2)
     
        H=W*A_a'+A_a*W-B_a*R-R'*B_a'
        
        v_W'*W*v_W - Epsilon1*eye(2*n) == semidefinite(2*n);

cvx_end

else %4b)4b

    Caso = 2
    cvx_begin
    
    variables p1 p2 W(4,4) R(2,4)
    
    minimize (p1+p2)
    
    subject to
        
        W(1,1)>=Epsilon1
        W(2,2)>=Epsilon1
        W(1,1)<=p1
        W(2,2)<=p1
        W(3,3)==W(1,1)
        W(4,4)==W(2,2)

        R(1,1)>=-p2
        R(1,1)<=p2
        R(2,3)==R(1,1)
        R(1,2)>=-p2
        R(1,2)<=p2
        R(2,4)==R(1,2)

        H=W*A_a'+A_a*W-B_a*R-R'*B_a'
        
        Epsilon2*eye(2*n) + v_H'*H*v_H == -semidefinite(2*n);        

cvx_end
end


R
W=full(W)
K=R/W