Optimality conditions for approximate Pareto solutions of a nonsmooth vector optimization problem with an infinite number of constraints

2018/08/30 by Ta Quang Son, Son, Ta Quang, Nguyễn Văn Tuyên +3
Computer Science · Mathematics · #41A65 #65K10 #90C29 #90C34 #90C46 #Advanced Optimization Algorithms Research #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.1808.10100

openalex publication_date 2018/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present some new necessary and sufficient optimality conditions in terms of the Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of constraints. As a consequence, we obtain optimality conditions for the particular cases of cone-constrained convex vector optimization problems and semidefinite vector optimization problems. Examples are given to illustrate the obtained results.

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