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

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

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.

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.

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