求解张量互补问题的一类光滑模系矩阵迭代方法

doi:10.12286/jssx.j2020-0732

计算数学 ›› 2022, Vol. 44 ›› Issue (2): 178-186.DOI: 10.12286/jssx.j2020-0732

求解张量互补问题的一类光滑模系矩阵迭代方法

宋珊珊, 李郴良

桂林电子科技大学数学与计算科学学院, 广西高校数据分析与计算重点实验室, 桂林 541004

收稿日期:2020-08-31 出版日期:2022-05-14 发布日期:2022-05-06
基金资助:
国家自然科学基金项目(11661027),国家重大仪器专项(61627807)和广西自然科学基金项目(2020GXNSFAA159143)资助.

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宋珊珊, 李郴良. 求解张量互补问题的一类光滑模系矩阵迭代方法[J]. 计算数学, 2022, 44(2): 178-186.

Song Shanshan, Li Chenliang. A CLASS OF SMOOTH MODULUS-BASED MATRIX ITERATION METHODS FOR SOLVING TENSOR COMPLEMENTARITY PROBLEM[J]. Mathematica Numerica Sinica, 2022, 44(2): 178-186.

A CLASS OF SMOOTH MODULUS-BASED MATRIX ITERATION METHODS FOR SOLVING TENSOR COMPLEMENTARITY PROBLEM

Song Shanshan, Li Chenliang

School of Mathematics and Computational Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin 541004, China

Received:2020-08-31 Online:2022-05-14 Published:2022-05-06

本文提出了求解张量互补问题的一类光滑模系矩阵迭代方法.其基本思想是,先将张量互补问题转化为等价的模系方程组,然后引入一个逼近的光滑函数进行求解.我们分析了算法的收敛性,并通过数值实验验证了所提出算法的有效性.

关键词： 张量互补问题, 光滑模系矩阵迭代方法, 光滑函数

In this paper, we present a class of smoothing modulus-based matrix iteration methods for solving the tensor complementarity problem. The basic idea is that, we firstly transform the tensor complementarity problem into an equivalent system of modulus-based equations, then introduce an approximated smoothing functions to obtain its approximation solutions. We analyze the convergence of the algorithms and verify the efficiency of the proposed algorithms by numerical experiments.

Key words: tensor complementarity problem, smooth modulus-based matrix iteration methods, smoothing function

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求解张量互补问题的一类光滑模系矩阵迭代方法

A CLASS OF SMOOTH MODULUS-BASED MATRIX ITERATION METHODS FOR SOLVING TENSOR COMPLEMENTARITY PROBLEM

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