Max_{w} \log(|h^Hw|^2) is a concave function

Nonconvex
1

But I got this error

Warning: A non-empty cvx problem already exists in this scope.
It is being overwritten.

In cvxprob (line 28)
In cvx_begin (line 41)
Error using cvx/log (line 64)
Disciplined convex programming error:
Illegal operation: log( {convex} ).

How can I sort this out?

Kind regards,
yunus

2

The simplified problem is

cvx_begin quiet
variable wy(20,1)
maximize log(wy’*wy)
subject to
power(2,norm(wy(1:4),2))<= EHp
cvx_end

where EHp is a constant.

4

Welcome to the forum!!

For dimension 2 or greater, that objective is neither convex nor concave, hence is not allowed in CVX.

Let wy be 2 by 1 (and h = 1). The objective is log(wy(1)^2+wy(2)^2). Its Hessian evaluated at w(1) = w(2) = 1 has eigenvalues of -1 and 1. QED.

1 Like
5

Many thanks for your time and clear answer!

Kind regards