Existence of Weak Pareto Efficient Solutions of a Vector Optimization Problem under a Closed Constraint Set

2024/08/08 by Danyang Liu, Jun Li, Liu, Danyang +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2408.04352

openalex publication_date 2024/08/08 · openalex created_date 2024/10/16 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the nonemptiness of weak Pareto efficient solution set for a class of nonsmooth vector optimization problems on a nonempty closed constraint set without any boundedness and convexity assumptions. First, we obtain a new property concerning the nonemptiness of weak Pareto efficient solution sets for these vector optimization problems. Then, under the condition of weak section-boundedness from below, we establish relationships between the notions of properness, Palais-Smale, weak Palais-Smale and M-tameness conditions with respect to some index sets for the restriction of the vector mapping on the constraint set. Finally, we present some new necessary and sufficient conditions for the nonemptiness of the weak Pareto efficient solution set for a general class of nonsmooth vector optimization problems.

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• Existence of Solutions and Relative Regularity Conditions for Polynomial Vector Optimization Problems

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