Arcwise connected functions and applications in multiobjective optimization

Abstract

We have given a generalization of arcwise connected functions, the concept of which was originally introduced by Avriel and Zang, taking values in the Euclidean Space with a given preference order. Such a generalization has the potential of obtaining local-global optimal properties of solutions of the multiple objective optimization problem in a more general setting. The results of this work can be specialized to give quite a few earlier results on such functions used in the case of single objective optimization problem obtained by several authors mentioned in the introduction.