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

IF 1.3 4区数学 Q2 MATHEMATICS, APPLIED

Optimization Letters 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

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.