Treatment of Set-Valued Robustness via Separation and Scalarization

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-13 DOI:10.1007/s10957-024-02423-4

Madhusudan Das, Chandal Nahak, Mahendra Prasad Biswal

引用次数: 0

Abstract

This paper aims to present alternative characterizations for different types of set-valued robustness concepts. Equivalent scalar representations for various set order relations are derived when the sets are the union of sets. Utilizing these findings in conjunction with image space analysis, specific isolated sets are defined for different notions of robust solutions. These isolated sets serve as the basis for deriving both necessary and sufficient robust optimality conditions. The validity of the results is demonstrated through several illustrative examples. Additionally, the paper concludes with an application of our present approach to two-player zero-sum matrix games.

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通过分离和标量化处理集值鲁棒性

本文旨在提出不同类型的集合值稳健性概念的替代表征。当集合是集合的联合时，各种集合顺序关系的等价标量表示被推导出来。利用这些发现和图像空间分析，为不同的鲁棒性解决方案概念定义了特定的孤立集。这些孤立集是推导必要和充分稳健优化条件的基础。本文通过几个示例证明了这些结果的有效性。此外，本文最后还将本方法应用于双人零和矩阵博弈。

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.