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

Nonconvex
4

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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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