A Generalized $$\Gamma $$ -Convergence Concept for a Class of Equilibrium Problems

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED Journal of Nonlinear Science Pub Date : 2024-07-05 DOI:10.1007/s00332-024-10059-x

Michael Hintermüller, Steven-Marian Stengl

引用次数: 0

Abstract

A novel generalization of $\Gamma $-convergence applicable to a class of equilibrium problems is studied. After the introduction of the latter, a variety of its applications is discussed. The existence of equilibria with emphasis on Nash equilibrium problems is investigated. Subsequently, our $\Gamma $-convergence notion for equilibrium problems is introduced and discussed as well as applied to a class of penalized generalized Nash equilibrium problems and quasi-variational inequalities. The work ends with a comparison of our results to previous generalizations in the literature.

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一类均衡问题的广义 $$\Gamma $$ 收敛概念

研究了适用于一类平衡问题的（\γ\）收敛的新概括。在介绍了后者之后，讨论了它的各种应用。重点研究了纳什均衡问题的均衡存在性。随后，引入并讨论了我们对均衡问题的 $\Gamma $-收敛概念，并将其应用于一类受惩罚的广义纳什均衡问题和准变量不等式。最后，将我们的结果与之前文献中的概括进行了比较。

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 Nonlinear Science 数学-力学

CiteScore

5.00

自引率

3.30%

发文量

审稿时长

4.5 months

期刊介绍： The mission of the Journal of Nonlinear Science is to publish papers that augment the fundamental ways we describe, model, and predict nonlinear phenomena. Papers should make an original contribution to at least one technical area and should in addition illuminate issues beyond that area''s boundaries. Even excellent papers in a narrow field of interest are not appropriate for the journal. Papers can be oriented toward theory, experimentation, algorithms, numerical simulations, or applications as long as the work is creative and sound. Excessively theoretical work in which the application to natural phenomena is not apparent (at least through similar techniques) or in which the development of fundamental methodologies is not present is probably not appropriate. In turn, papers oriented toward experimentation, numerical simulations, or applications must not simply report results without an indication of what a theoretical explanation might be. All papers should be submitted in English and must meet common standards of usage and grammar. In addition, because ours is a multidisciplinary subject, at minimum the introduction to the paper should be readable to a broad range of scientists and not only to specialists in the subject area. The scientific importance of the paper and its conclusions should be made clear in the introduction-this means that not only should the problem you study be presented, but its historical background, its relevance to science and technology, the specific phenomena it can be used to describe or investigate, and the outstanding open issues related to it should be explained. Failure to achieve this could disqualify the paper.