# Famous convex maximization problems

Which are the most famous problems having an objective of maximizing a nonlinear convex function (or minimizing a concave function)? As far as I know such an objective with respect to linear constraints is np-hard.

• Adding to the answer: Max-CUT problem is re-formulated as $$\max \frac{1}{4} x^T L x \\ s.t. \ x \in [-1,1]^n$$ where L is the Laplacian form of the graph, which is a PSD matrix. So this is another nice example. Nov 18 '18 at 20:47