According to cvx user’s guide the function pos(x) is convex but I am not sure either it’s still convex if we apply the frobenius norm.
Here is my problem in cvx
Y=rand(5,3);
B=rand(5,3);
X=rand(3,3);
cvx_begin sdp
variables A(5,3)
minimize(norm(pos(A*X+B)-Y,‘fro’))
cvx_end
and it returns the following error:
Disciplined convex programming error:
Cannot perform the operation norm( {convex}, 2 )
I know that the h=f\circ g is convex if the hessian of g is positive semidefinite and in my example the hessian of pos(A*X+B)-Y with respect to A I am not sure about its semidefiniteness.