Optimality conditions in convex multiobjective SIP

TL;DR

This paper characterizes various types of efficient solutions in convex multiobjective semi-infinite programming, introducing new data qualifications and optimality conditions involving KKT multipliers and a novel gap function.

Contribution

It provides new optimality conditions and data qualifications for convex multiobjective semi-infinite programming problems, extending existing theory.

Findings

Characterization of weak, efficient, and isolated efficient solutions

Introduction of new data qualifications for optimality conditions

Development of a new gap function for solution analysis

Abstract

The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely many convex constraints. To do this, we introduce new and already known data qualifications (conditions involving the constraints and/or the objectives) in order to get optimality conditions which are expressed in terms of either Karusk-Kuhn-Tucker multipliers or a new gap function associated with the given problem.