A New Path-Following Algorithm for Nonlinear P∗ Complementarity Problems

Y. B. ZHAO; D. LI

doi:10.1007/s10589-005-3905-y

A New Path-Following Algorithm for Nonlinear P∗ Complementarity Problems

Y. B. ZHAO
, D. LI

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

9 Citations (Scopus)

Abstract

Based on the recent theoretical results of Zhao and Li [Math. Oper. Res., 26 (2001), pp. 119-146], we present in this paper a new path-following method for nonlinear P∗ complementarity problems. Different from most existing interior-point algorithms that are based on the central path, this algorithm tracks the "regularized central path" which exists for any continuous P∗ problem. It turns out that the algorithm is globally convergent for any P∗ problem provided that its solution set is nonempty. By different choices of the parameters in the algorithm, the iterative sequence can approach to different types of points of the solution set. Moreover, local superlinear convergence of this algorithm can also be achieved under certain conditions.

Original language	English
Pages (from-to)	183-214
Journal	Computational Optimization and Applications
Volume	34
Issue number	2
Online published	23 Mar 2006
DOIs	https://doi.org/10.1007/s10589-005-3905-y
Publication status	Published - Jun 2006
Externally published	Yes

Research Keywords

Nonlinear complementarity problems
P∗-mappings
Path-following algorithms
Regularized central path
Tikhonov regularization

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10.1007/s10589-005-3905-y

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title = "A New Path-Following Algorithm for Nonlinear P∗ Complementarity Problems",

abstract = "Based on the recent theoretical results of Zhao and Li [Math. Oper. Res., 26 (2001), pp. 119-146], we present in this paper a new path-following method for nonlinear P∗ complementarity problems. Different from most existing interior-point algorithms that are based on the central path, this algorithm tracks the {"}regularized central path{"} which exists for any continuous P∗ problem. It turns out that the algorithm is globally convergent for any P∗ problem provided that its solution set is nonempty. By different choices of the parameters in the algorithm, the iterative sequence can approach to different types of points of the solution set. Moreover, local superlinear convergence of this algorithm can also be achieved under certain conditions.",

keywords = "Nonlinear complementarity problems, P∗-mappings, Path-following algorithms, Regularized central path, Tikhonov regularization",

author = "ZHAO, \{Y. B.\} and D. LI",

year = "2006",

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doi = "10.1007/s10589-005-3905-y",

language = "English",

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journal = "Computational Optimization and Applications",

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TY - JOUR

T1 - A New Path-Following Algorithm for Nonlinear P∗ Complementarity Problems

AU - ZHAO, Y. B.

AU - LI, D.

PY - 2006/6

Y1 - 2006/6

N2 - Based on the recent theoretical results of Zhao and Li [Math. Oper. Res., 26 (2001), pp. 119-146], we present in this paper a new path-following method for nonlinear P∗ complementarity problems. Different from most existing interior-point algorithms that are based on the central path, this algorithm tracks the "regularized central path" which exists for any continuous P∗ problem. It turns out that the algorithm is globally convergent for any P∗ problem provided that its solution set is nonempty. By different choices of the parameters in the algorithm, the iterative sequence can approach to different types of points of the solution set. Moreover, local superlinear convergence of this algorithm can also be achieved under certain conditions.

AB - Based on the recent theoretical results of Zhao and Li [Math. Oper. Res., 26 (2001), pp. 119-146], we present in this paper a new path-following method for nonlinear P∗ complementarity problems. Different from most existing interior-point algorithms that are based on the central path, this algorithm tracks the "regularized central path" which exists for any continuous P∗ problem. It turns out that the algorithm is globally convergent for any P∗ problem provided that its solution set is nonempty. By different choices of the parameters in the algorithm, the iterative sequence can approach to different types of points of the solution set. Moreover, local superlinear convergence of this algorithm can also be achieved under certain conditions.

KW - Nonlinear complementarity problems

KW - P∗-mappings

KW - Path-following algorithms

KW - Regularized central path

KW - Tikhonov regularization

UR - https://www.scopus.com/pages/publications/33745127413

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-33745127413&origin=recordpage

U2 - 10.1007/s10589-005-3905-y

DO - 10.1007/s10589-005-3905-y

M3 - RGC 21 - Publication in refereed journal

SN - 0926-6003

VL - 34

SP - 183

EP - 214

JO - Computational Optimization and Applications

JF - Computational Optimization and Applications

IS - 2

ER -

A New Path-Following Algorithm for Nonlinear P∗ Complementarity Problems

Abstract

Research Keywords

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Erratum: A new path-following algorithm for nonlinear P* complementarity problems (Computational Optimization and Applications (2006) 34:2 (183-214) DOI: 10.1007/s10589-005-3905-y)

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