Levenberg-Marquardt method for absolute value equation associated with second-order cone

IF 1.1 Q2 MATHEMATICS, APPLIED

Numerical Algebra Control and Optimization Pub Date : 2022-01-01 DOI:10.3934/naco.2021050

Xin He Miao, Kai Yao, Ching-Yu Yang, Jein-Shan Chen

引用次数: 6

Abstract

In this paper, we suggest the Levenberg-Marquardt method with Armijo line search for solving absolute value equations associated with the second-order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. We analyze the convergence of the proposed algorithm. For numerical reports, we not only show the efficiency of the proposed method, but also present numerical comparison with smoothing Newton method. It indicates that the proposed algorithm could also be a good choice for solving the SOCAVE.

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二阶锥相关绝对值方程的Levenberg-Marquardt方法

在本文中，我们提出了用Armijo线搜索的Levenberg-Marquardt方法来求解与二阶锥相关的绝对值方程(简称SOCAVE)，这是近十年来文献中经常讨论的标准绝对值方程的推广。分析了该算法的收敛性。通过数值计算，不仅证明了该方法的有效性，而且还与光滑牛顿法进行了数值比较。这表明该算法也可以作为求解SOCAVE的一个很好的选择。

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

Numerical Algebra Control and Optimization MATHEMATICS, APPLIED-

CiteScore

3.10

自引率

0.00%

发文量

期刊介绍： Numerical Algebra, Control and Optimization (NACO) aims at publishing original papers on any non-trivial interplay between control and optimization, and numerical techniques for their underlying linear and nonlinear algebraic systems. Topics of interest to NACO include the following: original research in theory, algorithms and applications of optimization; numerical methods for linear and nonlinear algebraic systems arising in modelling, control and optimisation; and original theoretical and applied research and development in the control of systems including all facets of control theory and its applications. In the application areas, special interests are on artificial intelligence and data sciences. The journal also welcomes expository submissions on subjects of current relevance to readers of the journal. The publication of papers in NACO is free of charge.