A global optimization approach to Berge equilibrium based on a regularized function

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED Optimization Letters Pub Date : 2024-07-30 DOI:10.1007/s11590-024-02141-w

G. Battur, S. Batbileg, R. Enkhbat

引用次数: 0

Abstract

This work deals with a Berge equilibrium problem (BEP). Based on the existence results of Berge equilibrium of Nessah et al. (Appl Math Lett 20(8):926–932. 2007), we consider BEP with concave objective functions. The existence of Berge equilibrium has been proven. BEP reduces to nonsmooth optimization problem. Then using a regularized function, we reduce a problem of finding Berge equilibrium to a nonconvex global optimization problem with a differentiable objective functions. The later allows to apply optimization methods and algorithms to solve the original problem.

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基于正则函数的 Berge 平衡全局优化方法

本研究涉及 Berge 平衡问题 (BEP)。基于 Nessah 等人的 Berge 平衡存在性结果（Appl Math Lett 20(8):926-932.2007）的基础上，我们考虑了具有凹目标函数的 BEP。Berge 平衡的存在已被证明。BEP 简化为非光滑优化问题。然后，利用正则化函数，我们将寻找 Berge 平衡的问题简化为具有可微目标函数的非凸全局优化问题。之后，我们就可以应用优化方法和算法来解决原始问题。

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

Optimization Letters 管理科学-应用数学

CiteScore

3.40

自引率

6.20%

发文量

116

审稿时长

9 months

期刊介绍： Optimization Letters is an international journal covering all aspects of optimization, including theory, algorithms, computational studies, and applications, and providing an outlet for rapid publication of short communications in the field. Originality, significance, quality and clarity are the essential criteria for choosing the material to be published. Optimization Letters has been expanding in all directions at an astonishing rate during the last few decades. New algorithmic and theoretical techniques have been developed, the diffusion into other disciplines has proceeded at a rapid pace, and our knowledge of all aspects of the field has grown even more profound. At the same time one of the most striking trends in optimization is the constantly increasing interdisciplinary nature of the field. Optimization Letters aims to communicate in a timely fashion all recent developments in optimization with concise short articles (limited to a total of ten journal pages). Such concise articles will be easily accessible by readers working in any aspects of optimization and wish to be informed of recent developments.