复择定理及元引理的一些推广

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Set-Valued and Variational Analysis Pub Date : 2022-05-18 DOI:10.1007/s11228-022-00641-4

Ahmed Roubi

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引用次数: 1

摘要

本文讨论了不等式系统的可选定理。确切地说，我们给出了一个公式，它包含了几个已知的替代定理，并将它们的处理统一在一个极大极小等式假设下，这个假设是由一系列函数族实现的。将元引理推广到具有若干一般函数且满足极大极小定理的系统，以及若干二次函数的特殊系统。

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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Theorems of the Alternative Revisited and Some Extensions of Yuan’s Lemma

In this paper we deal with theorems of the alternative for systems of inequalities. Precisely, we give a formulation that encompasses several known alternative theorems and unifies their treatment under a minimax equality assumption which is fulfilled by a whole panoply of families of functions. We also give extensions of Yuan’s lemma to systems with several general functions provided that they fulfill a certain minimax theorem, and to some particular systems of several quadratic functions.

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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.