A Generalization of Normal Sets

Abstract

Monotonic optimization is one of specially structured nonconvex problems that is frequently used in <br><br>application. Many nonconvex optimization problems in engineering could be directly converted to a <br><br>monotonic optimization problem. Polyblock approximation algorithm is the early solution method for these <br><br>problems. This algorithm is mainly based on the concept of normal sets. In this paper we propose a <br><br>generalization of normal sets. We show that some theoretical results on already defined normal sets are true <br><br>in the new context. This extension permits us to model more optimization problems in the monotonic <br><br>optimization framework.