A Generalization of Normal Sets

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