Continuity of the solutions sets for parametric set optimization problems

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-04-30 DOI:10.1186/s13660-024-03138-w

Manli Yang, Taiyong Li, Guanghui Xu

引用次数: 0

Abstract

The current study focuses on exploring the stability of solution sets pertaining to set optimization problems, particularly with regard to the set order relation outlined by Karaman et al. 2018. Sufficient conditions are provided for the lower semicontinuity, upper semicontinuity, and compactness of m-minimal solution mappings in parametric set optimization, where the involved set-valued mapping is Lipschitz continuous.

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参数集优化问题解集的连续性

目前的研究侧重于探索与集合优化问题有关的解集的稳定性，特别是与卡拉曼等人 2018 年概述的集合阶次关系有关的解集的稳定性。本研究为参数集优化中 m 最小解映射的下半连续性、上半连续性和紧凑性提供了充分条件，其中涉及的集值映射是 Lipschitz 连续的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.