涉及Minkowski差分的集合拟优化问题解的存在性

IF 1.4 4区数学 Q2 MATHEMATICS, APPLIED Numerical Functional Analysis and Optimization Pub Date : 2023-07-15 DOI:10.1080/01630563.2023.2233585

Lê Anh Tuấn

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引用次数: 0

摘要

摘要本文给出了一类包含Minkowski差分的集拟优化问题解存在的可验证条件，其中目标映射定义在完备度量空间中。我们的证明方法不基于任何标量化方法，我们的存在性结果是根据问题的给定数据写成的。提供了几个示例。作为本文主要结果的应用，给出了集值映射不确定多目标拟优化问题鲁棒解存在性的新结果。

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Existence of Solutions of Set Quasi-Optimization Problems Involving Minkowski Difference

Abstract This paper gives verifiable conditions for the existence of solutions of some set quasi-optimization problems involving Minkowski difference, where the objective maps are defined in complete metric spaces. Our proof method is not based on any scalarizing approach, and our existence results are written in terms of the given data of the problems. Several examples are provided. As applications of the main results of this paper, new results on the existence of robust solutions for uncertain multi-objective quasi-optimization problems with set-valued maps are formulated.

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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.