Weak-stability and saddle point theorems for a multiobjective optimization problem with an infinite number of constraints

Abstract

In this paper, we focus on weak-stability and saddle point theorems of multiobjective optimization problemsthat have an infinite number of constraints. The obtained results are based on the notion of weak-subdifferentials forvector functions. Some properties of weak stability for the problems are introduced. Relationships between strong dualityand saddle points of the augmented Lagrange vector functions associated to the problems are investigated. Connectionsbetween weak-stability and saddle point theorems of the problems are established. An example is given.