Generalized Convexity in Multiobjective Programming

Abstract

For the scalar programming problem, some characterizations for optimal solutions are known. In these characterizations convexity properties play a very important role. In this work, we study characterizations for multiobjective programming problem solutions when functions belonging to the problem are differentiable. These characterizations need some conditions of convexity. In differentiable scalar programming problems the concept of invexity is very important. We prove that it is also necessary for the multiobjective programming problem and give some characterizations of multiobjective programming problem solutions under weaker conditions. We define analogous concepts to those of stationary points and to the conditions of Kuhn-Tucker and Fritz-John for the multiobjective programming problem. © 1999 Academic Press.