New smooth weighted complementarity functions and a cubically convergent method for wLCP

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-24 DOI:10.1007/s11590-024-02139-4

Tiantian Fan, Jingyong Tang

引用次数: 0

Abstract

The weighted linear complementarity problem (wLCP) can be used for modelling a large class of problems from science and economics. In this paper, we introduce a new class of weighted complementarity functions and show that it is continuously differentiable everywhere. By using this function, we propose a two steps Levenberg–Marquardt-type method to solve the wLCP. Under suitable conditions, we prove that the proposed method is globally convergent and the generated iteration sequence is bounded. Moreover, we show that the proposed method has cubic convergence rate under the local error bound condition. Some numerical results are reported.

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新的平滑加权互补函数和 wLCP 的立方收敛方法

加权线性互补问题（wLCP）可用于模拟科学和经济学中的一大类问题。在本文中，我们引入了一类新的加权互补函数，并证明它在任何地方都是连续可微的。利用该函数，我们提出了一种两步 Levenberg-Marquardt 型方法来求解 wLCP。在合适的条件下，我们证明了所提出的方法是全局收敛的，并且所产生的迭代序列是有界的。此外，我们还证明了所提方法在局部误差约束条件下具有立方收敛率。我们还报告了一些数值结果。

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

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.