Scalarization of vectorial relations applied to certain optimization problems

Abstract

In this paper we consider certain optimization problems which are described by inequalities in partially ordered vector space.Using the scalarization procedure developed in [6,7] we derive optimality conditions for optimization problems of maximum type and for vector optimization problems. As applications we obtain various optimality conditions including an alternation theorem for the Chebyshev approximation with certain side-conditions and a scalarization for vector optimization problems where efficiency is defined by a cone.