Nonlinear scalarization in set optimization based on the concept of null set

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-03-20 DOI:10.1007/s10898-024-01385-1

Anveksha Moar, Pradeep Kumar Sharma, C. S. Lalitha

引用次数: 0

Abstract

The aim of this paper is to introduce a nonlinear scalarization function in set optimization based on the concept of null set which was introduced by Wu (J Math Anal Appl 472(2):1741–1761, 2019). We introduce a notion of pseudo algebraic interior of a set and define a weak set order relation using the concept of null set. We investigate several properties of this nonlinear scalarization function. Further, we characterize the set order relations and investigate optimality conditions for solution sets in set optimization based on the concept of null set. Finally, a numerical example is provided to compute a weak minimal solution using this nonlinear scalarization function.

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基于空集概念的集合优化中的非线性标量化

本文旨在基于吴文俊（J Math Anal Appl 472(2):1741-1761, 2019）提出的空集概念，引入集合优化中的非线性标量化函数。我们引入了一个集合的伪代数内部的概念，并利用空集的概念定义了一个弱集序关系。我们研究了这个非线性标量化函数的几个性质。此外，我们还根据空集的概念描述了集合秩关系，并研究了集合优化中解集的最优性条件。最后，我们提供了一个数值示例，利用这种非线性标量化函数计算弱最小解。

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.

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