On New Generalized Differentials with Respect to a Set and Their Applications

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Set-Valued and Variational Analysis Pub Date : 2024-08-14 DOI:10.1007/s11228-024-00729-z

Xiaolong Qin, Vo Duc Thinh, Jen-Chih Yao

引用次数: 0

Abstract

The notions and certain fundamental characteristics of the proximal and limiting normal cones with respect to a set are first presented in this paper. We present the ideas of the limiting coderivative and subdifferential with respect to a set of multifunctions and singleton mappings, respectively, based on these normal cones. The necessary and sufficient conditions for the Aubin property with respect to a set of multifunctions are then described by using the limiting coderivative with respect to a set. As a result of the limiting subdifferential with respect to a set, we offer the requisite optimality criteria for local solutions to optimization problems. In addition, we also provide examples to demonstrate the outcomes.

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论关于集合的新广义微分及其应用

本文首先介绍了关于集合的近似法锥和极限法锥的概念和某些基本特征。在这些法锥的基础上，我们分别提出了相对于多元函数集合和单子映射的极限编码微分和子微分的思想。然后，利用相对于集合的极限编衍描述了相对于多元函数集合的奥宾性质的必要条件和充分条件。作为关于集合的极限次微分的结果，我们为优化问题的局部解提供了必要的最优性标准。此外，我们还举例说明了这些成果。

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

Set-Valued and Variational Analysis MATHEMATICS, APPLIED-

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： The scope of the journal includes variational analysis and its applications to mathematics, economics, and engineering; set-valued analysis and generalized differential calculus; numerical and computational aspects of set-valued and variational analysis; variational and set-valued techniques in the presence of uncertainty; equilibrium problems; variational principles and calculus of variations; optimal control; viability theory; variational inequalities and variational convergence; fixed points of set-valued mappings; differential, integral, and operator inclusions; methods of variational and set-valued analysis in models of mechanics, systems control, economics, computer vision, finance, and applied sciences. High quality papers dealing with any other theoretical aspect of control and optimization are also considered for publication.