Extended LQP Method for Monotone Nonlinear Complementarity Problems

To solve nonlinear complementarity problems (NCP), the logarithmic-quadratic proximal (LQP) method solves a system of nonlinear equations at each iteration. In this paper, the iterates generated by the original LQP method are extended by explicit formulas and thus an extended LQP method is presented...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 135; no. 3; pp. 343 - 353
Main Authors BNOUHACHEM, A, YUAN, X. M
Format Journal Article
LanguageEnglish
Published New York, NY Springer 01.12.2007
Springer Nature B.V
Subjects
Applied sciences
Exact sciences and technology
Iterative methods
Lower bounds
Management science
Mathematical models
Mathematical programming
Nonlinear equations
Nonlinearity
Operational research and scientific management
Operational research. Management science
Optimization
Studies
Proximal
Lower bound
Logarithmic function
Nonlinear complementarity problems
Non linear complementarity problem
Non linear system
Modeling
Logarithmic-quadratic proximal method
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Summary:To solve nonlinear complementarity problems (NCP), the logarithmic-quadratic proximal (LQP) method solves a system of nonlinear equations at each iteration. In this paper, the iterates generated by the original LQP method are extended by explicit formulas and thus an extended LQP method is presented. It is proved theoretically that the lower bound of the progress obtained by the extended LQP method is greater than that by the original LQP method. Preliminary numerical results are provided to verify the theoretical assertions and the effectiveness of both the original and the extended LQP method.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-007-9287-9