An R -linearly convergent derivative-free algorithm for nonlinear complementarity problems based on the generalized Fischer–Burmeister merit function

In the paper [J.-S. Chen, S. Pan, A family of NCP-functions and a descent method for the nonlinear complementarity problem, Computational Optimization and Applications, 40 (2008) 389–404], the authors proposed a derivative-free descent algorithm for nonlinear complementarity problems (NCPs) by the g...

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Vydané v:Journal of computational and applied mathematics Ročník 232; číslo 2; s. 455 - 471
Hlavní autori: Chen, Jein-Shan, Gao, Hung-Ta, Pan, Shaohua
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Kidlington Elsevier B.V 15.10.2009
Elsevier
Predmet:
Calculus of variations and optimal control
Convergence rate
Exact sciences and technology
Functional analysis
Functions of a complex variable
Global error bound
Mathematical analysis
Mathematics
Merit function
NCP-function
Nonlinear complementarity problem
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Sciences and techniques of general use
Convergence rate
Nonlinear complementarity problem
Global error bound
Merit function
NCP-function
Error estimation
Convergence acceleration
Optimization method
Complementarity problem
Nonlinear problems
Algorithm
Penalty method
Convergence
Numerical analysis
Algorithm performance
Applied mathematics
Descent method
Mathematical programming
ISSN:0377-0427, 1879-1778
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Popis
Shrnutí:In the paper [J.-S. Chen, S. Pan, A family of NCP-functions and a descent method for the nonlinear complementarity problem, Computational Optimization and Applications, 40 (2008) 389–404], the authors proposed a derivative-free descent algorithm for nonlinear complementarity problems (NCPs) by the generalized Fischer–Burmeister merit function: ψ p ( a , b ) = 1 2 [ ‖ ( a , b ) ‖ p − ( a + b ) ] 2 , and observed that the choice of the parameter p has a great influence on the numerical performance of the algorithm. In this paper, we analyze the phenomenon theoretically for a derivative-free descent algorithm which is based on a penalized form of ψ p and uses a different direction from that of Chen and Pan. More specifically, we show that the algorithm proposed is globally convergent and has a locally R -linear convergence rate, and furthermore, its convergence rate will become worse when the parameter p decreases. Numerical results are also reported for the test problems from MCPLIB, which further verify the theoretical results obtained.
Bibliografia:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2009.06.022