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

IF 1.8 3区数学 Q1 Mathematics

Journal of Global Optimization 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

Journal of Global Optimization 数学-应用数学

CiteScore

0.10

自引率

5.60%

发文量

137

审稿时长

6 months

期刊介绍： The Journal of Global Optimization publishes carefully refereed papers that encompass theoretical, computational, and applied aspects of global optimization. While the focus is on original research contributions dealing with the search for global optima of non-convex, multi-extremal problems, the journal’s scope covers optimization in the widest sense, including nonlinear, mixed integer, combinatorial, stochastic, robust, multi-objective optimization, computational geometry, and equilibrium problems. Relevant works on data-driven methods and optimization-based data mining are of special interest. In addition to papers covering theory and algorithms of global optimization, the journal publishes significant papers on numerical experiments, new testbeds, and applications in engineering, management, and the sciences. Applications of particular interest include healthcare, computational biochemistry, energy systems, telecommunications, and finance. Apart from full-length articles, the journal features short communications on both open and solved global optimization problems. It also offers reviews of relevant books and publishes special issues.