Dual SDP Problem from Its Primal

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2020 5 21

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Hey!

I am computing a probability distribution from some measurements and I used primal sdp method for that; but now I need to convert it to its dual. How can I do that with cvx?

My function for primal is that:

cvx_begin 
variable sigma_e(d^2,d^2,d) hermitian semidefinite
dual variables Z{d,d,m,m} 
S=cvx(0);
in=1;
for e=1:d
S=S+trace(sigma_e(:,:,e)*kron(A(:,:,in,e),eye(d)));
end
S=real(S);
minimize (-S)
subject to 
for i=1:d
    for j=1:d
       for x=1:m
            for y=1:m
                      
                
trace(squeeze(sum(sigma_e(:,:,:),3))*kron(A(:,:,x,i),B(:,:,y,j)))==P_exp(i,j,x,y) : Z{i,j,x,y};
          
            end
        end
    end
end
cvx_end