随机R0张量互补问题的投影Levenberg-Marquardt方法

doi:10.15960/j.cnki.issn.1007-6093.2021.04.006

运筹学学报 ›› 2021, Vol. 25 ›› Issue (4): 69-79.doi: 10.15960/j.cnki.issn.1007-6093.2021.04.006

随机R₀张量互补问题的投影Levenberg-Marquardt方法

崔丽媛¹, 杜守强¹^,*()

1. 青岛大学数学与统计学院, 山东青岛 266071

收稿日期:2019-10-29 出版日期:2021-12-15 发布日期:2021-12-11
通讯作者: 杜守强 E-mail:sqdu@qdu.edu.cn
作者简介:杜守强, E-mail: sqdu@qdu.edu.cn
基金资助:
国家自然科学基金(11671220)

Projected Levenberg-Marquardt method for stochastic R₀ tensor complementarity problems

Liyuan CUI¹, Shouqiang DU¹^,*()

1. School of Mathematics and Statistics, Qingdao University, Qingdao 266071, Shandong, China

Received:2019-10-29 Online:2021-12-15 Published:2021-12-11
Contact: Shouqiang DU E-mail:sqdu@qdu.edu.cn

摘要/Abstract

摘要：

本文考虑一类离散型随机$R_0$张量互补问题，利用Fischer-Burmeister函数将问题转化为约束优化问题，并用投影Levenberg-Marquardt方法对其进行了求解。在一般的条件下得到了该方法的全局收敛性，相关的数值实验表明了该方法的有效性。

关键词: 随机R₀张量互补问题, 投影Levenberg-Marquardt方法, 全局收敛, 线搜索

Abstract:

In this paper, we consider a class of stochastic R₀ tensor complementarity problems with finitely many elements. Firstly, we use Fischer-Burmeister function to transform the problem into a constrained optimization problem. Then a projected Levenberg-Marquardt method is used to solve the constrained optimization problem. Under general conditions, the global convergence of this method is proved, and the related numerical results show the efficiency of the method.

Key words: stochastic R₀ tensor complementarity problem, projected Levenberg-Marquardt method, global convergence, line search

中图分类号:

O221

崔丽媛, 杜守强. 随机R₀张量互补问题的投影Levenberg-Marquardt方法[J]. 运筹学学报, 2021, 25(4): 69-79.

Liyuan CUI, Shouqiang DU. Projected Levenberg-Marquardt method for stochastic R₀ tensor complementarity problems[J]. Operations Research Transactions, 2021, 25(4): 69-79.

图/表 3

表1

表2

表3

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$ x^* $	$ \mathrm{val} $	$ K $
$ (0, 0.258\, 8, 0.965\, 9)^{\rm T} $	$ 4.648\, 4\times10^{-17} $	$ 7 $
$ (0, 0.258\, 8, 0.965\, 9)^{\rm T} $	$ 1.941\, 6\times10^{-17} $	$ 6 $
$ (0, 0.258\, 8, 0.965\, 9)^{\rm T} $	$ 1.320\, 9\times10^{-17} $	$ 8 $
$ (0, 0.258\, 8, 0.965\, 9)^{\rm T} $	$ 3.957\, 6\times10^{-17} $	$ 8 $
$ (0, 0.258\, 8, 0.965\, 9)^{\rm T} $	$ 5.090\, 7\times10^{-17} $	$ 7 $

$ x^* $	$ \mathrm{val} $	$ K $
$ (0.001\, 2, 1.000\, 0, 0)^{\rm T} $	$ 2.511\, 0\times10^{-13} $	$ 10 $
$ (0.000\, 8, 1.000\, 0, 0)^{\rm T} $	$ 5.670\, 8\times10^{-14} $	$ 10 $
$ (0.000\, 7, 1.000\, 0, 0)^{\rm T} $	$ 3.154\, 5\times10^{-14} $	$ 10 $
$ (0.001\, 4, 1.000\, 0, 0)^{\rm T} $	$ 4.707\, 1\times10^{-13} $	$ 11 $
$ (0.001\, 3, 1.000\, 0, 0)^{\rm T} $	$ 3.835\, 6\times10^{-13} $	$ 9 $

$ x^* $	$ \mathrm{val} $	$ K $
$ (0.710\, 8, 0.170\, 9, 0.696\, 8, 0.014\, 9)^{\rm T} $	$ 9.832\, 1\times10^{-4} $	$ 340 $
$ (0.710\, 8, 0.170\, 9, 0.696\, 8, 0.014\, 9)^{\rm T} $	$ 9.832\, 1\times10^{-4} $	$ 166 $
$ (0.710\, 8, 0.170\, 9, 0.696\, 9, 0.014\, 9)^{\rm T} $	$ 9.832\, 1\times10^{-4} $	$ 397 $
$ (0.710\, 8, 0.170\, 9, 0.696\, 9, 0.014\, 9)^{\rm T} $	$ 9.832\, 1\times10^{-4} $	$ 200 $
$ (0.710\, 8, 0.170\, 9, 0.696\, 9, 0.014\, 9)^{\rm T} $	$ 9.832\, 1\times10^{-4} $	$ 353 $

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随机R₀张量互补问题的投影Levenberg-Marquardt方法

Projected Levenberg-Marquardt method for stochastic R₀ tensor complementarity problems

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