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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-07-15 DOI:10.1080/01630563.2023.2233585

Lê Anh Tuấn

引用次数: 0

Abstract

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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涉及Minkowski差分的集合拟优化问题解的存在性

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。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.