Maximization of linearly constrained posynomials

Abstract

This paper deals with the maximization of linearly constrained positive polynomials ( posynomials). While posynomials are not necessarily convex, they can be transformed to convex functions and thus the numerical maximization of such functions may result in the location of a local solution. We present a characterization of the global maximum for linearly constrained posynomials in terms of an associated nonlinear convex program. Also, we develop a hybrid algorithm based on a cutting plane and a modified gradient projection algorithm which guarantees the global maximum solution to this class of problems.