# Talk:Beginning with CVX

```lamda_W=eig(full(W))
```

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 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
```