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

12 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

Fingerprint

Keywords

Convergence rate
Mixed complementarity problem
Smoothing approximation
The generalized FB function

ASJC Scopus subject areas

Analysis
Applied Mathematics

Cite this

Chen, J-S., Pan, S., & Lin, T. C. (2010). A smoothing Newton method based on the generalized Fischer-Burmeister function for MCPs. Nonlinear Analysis, Theory, Methods and Applications, 72(9-10), 3739-3758. https://doi.org/10.1016/j.na.2010.01.012

@article{4f97b46cf4ee41d6a2066d316874f3bd,

title = "A smoothing Newton method based on the generalized Fischer-Burmeister function for MCPs",

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.",

keywords = "Convergence rate, Mixed complementarity problem, Smoothing approximation, The generalized FB function",

author = "Jein-Shan Chen and Shaohua Pan and Lin, {Tzu Ching}",

year = "2010",

month = may

day = "1",

doi = "10.1016/j.na.2010.01.012",

language = "English",

volume = "72",

pages = "3739--3758",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

publisher = "Elsevier Limited",

number = "9-10",

}

TY - JOUR

T1 - A smoothing Newton method based on the generalized Fischer-Burmeister function for MCPs

AU - Chen, Jein-Shan

AU - Pan, Shaohua

AU - Lin, Tzu Ching

PY - 2010/5/1

Y1 - 2010/5/1

N2 - 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.

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.

KW - Convergence rate

KW - Mixed complementarity problem

KW - Smoothing approximation

KW - The generalized FB function

UR - http://www.scopus.com/inward/record.url?scp=76549123306&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=76549123306&partnerID=8YFLogxK

U2 - 10.1016/j.na.2010.01.012

DO - 10.1016/j.na.2010.01.012

M3 - Article

AN - SCOPUS:76549123306

VL - 72

SP - 3739

EP - 3758

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

IS - 9-10

ER -

Access to Document

10.1016/j.na.2010.01.012