The relaxation modulus-based matrix splitting iteration methods for circular cone nonlinear complementarity problems

被引：27

作者：

Ke, Yi-Fen ^{[1
,2
,3
]}

Ma, Chang-Feng ^{[1
,2
]}

Zhang, Huai ^{[3
,4
]}

机构：

[1] Fujian Normal Univ, Coll Math & Informat, Fuzhou 350117, Fujian, Peoples R China

[2] Fujian Normal Univ, FJKLMAA, Fuzhou 350117, Fujian, Peoples R China

[3] Univ Chinese Acad Sci, Key Lab Computat Geodynam, Beijing 100049, Peoples R China

[4] Qingdao Natl Lab Marine Sci & Technol, Lab Marine Mineral Resources, Qingdao 266237, Peoples R China

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2018年 / 37卷 / 05期

基金：

中国博士后科学基金; 美国国家科学基金会;

关键词：

Circular cone; Nonlinear complementarity problem; Modulus method; Matrix splitting; Convergence; INTERIOR-POINT ALGORITHMS; SMOOTHING NEWTON METHOD; MERIT FUNCTIONS; 2ND-ORDER; CONVERGENCE;

D O I：

10.1007/s40314-018-0687-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a class of nonlinear complementarity problems associated with circular cone (CCNCP for short), which is a type of non-symmetric cone complementarity problems. Useful properties of the circular cone are investigated, which help to reformulate equivalently CCNCP as an implicit fixed-point equation. Based on the implicit fixed-point equation and splittings of the system matrix, we establish a class of relaxation modulus-based matrix splitting iteration methods for solving such a complementarity problem. The convergence of the proposed modulus-based matrix splitting iteration methods has been analyzed and the strategy choice of the parameters are discussed when the splitting matrix is symmetric positive definite. Numerical experiments have shown that the modulus-based iteration methods are effective for solving CCNCP.

引用

页码：6795 / 6820

页数：26