On the Solution of Generalized Multiplicative Extremum Problems

The paper addresses the problem of maximizing a sum of products of positive and concave real‐valued functions over a convex feasible set. A reformulation based on the image of the feasible set through the vector‐valued function which describes the problem, combined with an adequate application of convex analysis results, lead to an equivalent indefinite quadratic extremum problem with infinitely many linear constraints. Special properties of this later problem allow to solve it by an efficient relaxation algorithm. Some numerical tests illustrate the approach proposed.