准平衡问题的有限收敛和锐小值

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-30 DOI:10.1007/s10957-024-02454-x

Kanchan Mittal, Pankaj Gautam, Vellaichamy Vetrivel

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引用次数: 0

摘要

由 Polyak 提出的尖锐最小值概念是研究优化问题算法收敛分析的重要工具。对于变分不等式问题和均衡问题，人们已经进行了广泛的研究。本文将在尖锐最小值条件下建立准平衡问题（QEP）的近点法所产生序列的收敛性分析。此外，本文还提供了 QEP 弱尖锐解的特征。我们还引入了一种不精确的近点法，并证明了求解 QEP 时序列的收敛性。最后，我们推导了广义纳什均衡问题的近似点近似法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Finite Convergence and Sharp Minima for Quasi-Equilibrium Problems

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Finite Convergence and Sharp Minima for Quasi-Equilibrium Problems

The notion of sharp minima, given by Polyak, is an important tool in studying the convergence analysis of algorithms designed to solve optimization problems. It has been studied extensively for variational inequality problems and equilibrium problems. In this paper, the convergence analysis of the sequence generated by proximal point method for quasi-equilibrium problem (QEP) will be established under sharp minima conditions. Further, the characterizations of weak sharp solution for QEP are provided. We also introduce an inexact proximal point method and demonstrate the convergence of the sequence for solving the QEP. Finally, we deduce the proximal point approximation for generalized Nash equilibrium problem.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.