The projected splitting iterative methods based on tensor splitting and its majorization matrix splitting for the tensor complementarity problem

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED Optimization Letters Pub Date : 2024-03-24 DOI:10.1007/s11590-024-02104-1

Mengxiao Fan, Jicheng Li

引用次数: 0

Abstract

In this paper, we develop two kinds of the projected iterative methods for the tensor complementarity problem combining two different splitting frameworks. The first method is on the basis of tensor splitting, and its monotone convergence is proved based on the \({\mathcal{L}}\)-tensor and the strongly monotone tensor. Meanwhile, an alternative method is in the light of majorization matrix splitting, the convergence of which is given and is particularly analyzed based on the power Lipschitz tensor. Some numerical examples are tested to illustrate the proposed methods.

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基于张量分裂及其大化矩阵分裂的张量互补问题的投影分裂迭代法

在本文中，我们结合两种不同的分裂框架，为张量互补问题开发了两种投影迭代法。第一种方法以张量分裂为基础，基于 \({\mathcal{L}}\)- 张量和强单调张量证明了其单调收敛性。同时，根据大化矩阵分裂给出了另一种方法，并基于幂 Lipschitz 张量对其收敛性进行了分析。为了说明所提出的方法，还测试了一些数值示例。

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.