A smoothing Newton method based on the generalized Fischer-Burmeister function for MCPs

被引：17

作者：

Chen, Jein-Shan ^{[1
]}

Pan, Shaohua ^{[2
]}

Lin, Tzu-Ching ^{[1
]}

机构：

[1] Natl Taiwan Normal Univ, Dept Math, Taipei 11677, Taiwan

[2] S China Univ Technol, Sch Math Sci, Guangzhou 510640, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 9-10期

关键词：

Mixed complementarity problem; The generalized FB function; Smoothing approximation; Convergence rate; MIXED COMPLEMENTARITY-PROBLEMS; LEAST-SQUARES FORMULATION; DESCENT METHOD; NCP-FUNCTIONS; ALGORITHMS; CONVERGENCE;

D O I：

10.1016/j.na.2010.01.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a smooth approximation for the generalized Fischer-Burmeister function where the 2-norm in the FB function is relaxed to a general p-norm (p > 1), and establish some favorable properties for it - for example, the Jacobian consistency. With the smoothing function, we transform the mixed complementarity problem (MCP) into solving a sequence of smooth system of equations, and then trace a smooth path generated by the smoothing algorithm proposed by Chen (2000) [28] to the solution set. In particular, we investigate the influence of p on the numerical performance of the algorithm by solving all MCPLIP test problems, and conclude that the smoothing algorithm with p is an element of (1,2] has better numerical performance than the one with p > 2. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：3739 / 3758

页数：20

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