The L2 norm of a complex vector in cvx

Hi, I have a minimization problem in which the one of the inequality constraint is


however in cvx, I tried to use norm(h’ * v * v’), but it gives an error. It seems that CVX only accepts a square matrix. Is there any syntax I can use? at least any syntax i can use to make it work? approximation is okay as well. Due to the coupling of variables, I can not transform the vector v in to matrix V=v*v^H (like SDR).

That error message basically says you have one or more quadratic elements which are not recognizably convex due to being squares. It has nothing to do with whether a matrix has square dimensions.

You haven’t followed DCP rules. Moreover, your expression is non-convex (unless h is all zeros, or N=1), so reformulation to be acceptable to CVX is not possible. If there is a convex approximation suitable for your purposes, that is for you to determine, because it’s your problem, so you presumably know why you’re trying to solve it.

Hi Mark! Thank you for reply! I see. I will try to approximate it. Thanks again!