A New Topological Framework and Its Application to Well-Posedness in Set-Valued Optimization

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED

Numerical Functional Analysis and Optimization Pub Date : 2022-11-08 DOI:10.1080/01630563.2022.2141254

M. H. Geoffroy, James Larrouy

引用次数: 0

Abstract

Abstract In this paper, we introduce a topology on the power set of a partially ordered normed space Z from which we derive a topological convergence on along with new concepts of continuity and semicontinuity for set-valued mappings. Our goal is to propose an appropriate framework to address set optimization problems involving set relations based on a cone ordering. Taking advantage of this new setting, we establish several results regarding the well-posedness of set-valued optimization problems that are consistent with the state-of-the-art.

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一种新的拓扑框架及其在集值优化的适定性中的应用

摘要本文在部分有序赋范空间Z的幂集上引入了一种拓扑，由此导出了集值映射的拓扑收敛性，并给出了集值映射的连续性和半连续性的新概念。我们的目标是提出一个适当的框架来解决涉及基于锥排序的集合关系的集合优化问题。利用这个新的设置，我们建立了几个关于集值优化问题的适定性的结果，这些结果与最先进的一致。

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

Numerical Functional Analysis and Optimization 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Numerical Functional Analysis and Optimization is a journal aimed at development and applications of functional analysis and operator-theoretic methods in numerical analysis, optimization and approximation theory, control theory, signal and image processing, inverse and ill-posed problems, applied and computational harmonic analysis, operator equations, and nonlinear functional analysis. Not all high-quality papers within the union of these fields are within the scope of NFAO. Generalizations and abstractions that significantly advance their fields and reinforce the concrete by providing new insight and important results for problems arising from applications are welcome. On the other hand, technical generalizations for their own sake with window dressing about applications, or variants of known results and algorithms, are not suitable for this journal. Numerical Functional Analysis and Optimization publishes about 70 papers per year. It is our current policy to limit consideration to one submitted paper by any author/co-author per two consecutive years. Exception will be made for seminal papers.