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

Jein-Shan Chen; Shaohua Pan; Tzu Ching Lin

doi:10.1016/j.na.2010.01.012

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

Jein-Shan Chen, Shaohua Pan, Tzu Ching Lin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

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 ∈ (1, 2] has better numerical performance than the one with p > 2.

Original language	English
Pages (from-to)	3739-3758
Number of pages	20
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	72
Issue number	9-10
DOIs	https://doi.org/10.1016/j.na.2010.01.012
Publication status	Published - 2010 May 1

Keywords

Convergence rate
Mixed complementarity problem
Smoothing approximation
The generalized FB function

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2010.01.012

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abstract = "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 ∈ (1, 2] has better numerical performance than the one with p > 2.",

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AB - 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 ∈ (1, 2] has better numerical performance than the one with p > 2.

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