Second-order optimality conditions for multiobjective optimization problems with constraints

TL;DR

This paper develops second-order necessary optimality conditions for constrained multiobjective optimization problems using new second-order subdifferentials and variational analysis techniques.

Contribution

It introduces second-order subdifferentials for Gâteaux differentiable functions with Lipschitz derivatives and applies them to derive necessary conditions for weak Pareto solutions.

Findings

Second-order subdifferentials for specific classes of functions are defined.

Necessary conditions for weak Pareto optimality are established.

The approach extends variational analysis tools to multiobjective constrained problems.

Abstract

In this paper, we introduce the second-order subdifferentials for functions which are G\^ateaux differentiable on an open set and whose G\^ateaux derivative mapping is locally Lipschitz. Based on properties of this kind of second-order subdifferentials and techniques of variational analysis, we derive second-order necessary conditions for weak Pareto efficient solutions of multiobjective programming problems with constraints.