Dear All,

Note: I could not upload the all images since I am a new user so I am adding the link which you can access the the images which are including other information

https://ibb.co/PgBJVY6

https://ibb.co/PgBJVY6

My optimization problem is that:

I am tryin to write code for dual part. But I could not wirte. I mean the program is running but the result is wrong. Probably I could not write the S part correctly Could you please tell me where I am wrong

Best

```
function [G,W,S] = TD_P_inv_Dual(P_exp,T,A_ax,B_by)
d = size(P_exp,1);
m = size(P_exp,3);
%d = size(B_by,1);
%m = size(B_by,3);
cvx_begin
variable S(d,d,m,m)
%variable S2(1,m,m)
W_hat=zeros(d^2,d^2);
for a=1:d
for b=1:d
for x=1:m
for y=1:m
W_hat=W_hat+T(a,b,x,y).*(kron(A_ax(:,:,x,a),B_by(:,:,y,b)));
% if a ~= b
% S=sum(B(a,b,x,y));
% end
%W =W+S(1,x,y)* trace(sigma_e(:,:,a)*kron(A_ax(:,:,2,a),B_by(:,:,2,a)));
% W = trace(kron(A_ax(:,:,2,a),B_by(:,:,2,a)).*sigma_e(:,:,a))
end
end
end
end
W=sum(sum(sum(sum(T.*P_exp))));
J=cvx(0);
for a=1:d
for b =1:d
for x=1:m
for y =1:m
if a ~= b
S(a,b,x,y) == sum(T(a,b,x,y));
%W2=sum(W*S(a,b,x,y));
%disp(W2);
J=S(a,b,x,y).*W;
% W=sum(W*S(a,b,x,y));
%W=W*S(a,b,x,y)
end
end
end
end
end
% for x=1:m
% for y =1:m
%
% J=W*sum(S2(1,x,y));
% %J=W*S2(1,x,y);
% end
% end
%for e=1:d
% W = real(trace(W*rho));
% W = W*trace(sigma_e(:,:,3));
% W = trace(sigma_e(:,:,e)*W);
%end
%J= eye(d)+S*W;
J=real(J)
minimize(J)
subject to
for e=1:d
%(J-kron(squeeze(A_ax(:,:,1,e)),eye(d)))==semidefinite(d^2,d^2);
(J-kron(squeeze(A_ax(:,:,1,e)),eye(d)))==semidefinite(d^2,d^2);
end
%trace(squeeze(sum(S))*W_hat)==W;
cvx_end
S=double(S);
%S=cell2mat(S);
G=double(S(a,b,x,y).*W);
%G2=double(W*rho);
```