A modified LM algorithm for tensor complementarity problems over the circular cone

被引：3
|
作者：
Ke, Yifen [1 ,2 ,3 ,4 ]
Ma, Changfeng [1 ,2 ,3 ]
Zhang, Huai [1 ,2 ,4 ,5 ]
机构：
[1] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350117, Peoples R China
[2] Fujian Normal Univ, FJKLMAA, Fuzhou 350117, Peoples R China
[3] Ctr Appl Math Fujian Prov FJNU, Fuzhou 350117, Peoples R China
[4] Univ Chinese Acad Sci, Key Lab Computat Geodynam, Beijing 100049, Peoples R China
[5] Qingdao Natl Lab Marine Sci & Technol, Lab Marine Mineral Resources, Qingdao 266237, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2021年 / 398卷
基金：
中国国家自然科学基金;
关键词：
Tensor complementarity problem; Circular cone; Levenberg-Marquardt algorithm; Quadratic convergence; SMOOTHING NEWTON METHOD; INTERIOR-POINT ALGORITHMS; MATRIX-SPLITTING METHOD; MERIT FUNCTIONS; 2ND-ORDER; CONVERGENCE; EQUATIONS;
D O I：
10.1016/j.cam.2021.113689
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The tensor complementarity problem over circular cone (CCTCP for short) is studied, which is a specially structured nonlinear complementarity problem. Useful properties of the circular cone help to reformulate equivalently CCTCP as an implicit fixed-point equation. Based on the smoothing functions, we reformulate the obtained fixed-point equation as a family of parameterized smoothing equations. Moreover, we propose a modified Levenberg-Marquardt (LM) algorithm to solve the problem iteratively and show that the sequence generated by the new algorithm converges to a solution quadratically under suitable conditions. Preliminary numerical results demonstrate that the proposed algorithm is effective. (C) 2021 Elsevier B.V. All rights reserved.
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页数：21
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