A new smoothing method for nonlinear complementarity problems involving P0-function

Statistics, Optimization and Information Computing

article

El Hassene OSMANI¹  Mounir Haddou²  Naceurdine Bensalem³  Lina Abdallah⁴ 

[1] INSA-IRMAR Rennes and Laboratory of Fundamental and Numerical Mathematics, University Ferhat Abbas of Setif 1;Insa Rennes and IRMAR;Laboratory of Fundamental and Numerical Mathematics, University Ferhat Abbas of Setif 1;Lebanese University

关键词: Nonlinear complementarity problems;    Newton’s method;    smoothing functions;    P0-matrix;    interior-point methods;   

DOI  :  10.19139/soic-2310-5070-1493

来源: Istituto Superiore di Sanita

【 摘 要 】

In this paper, we present a family of smoothing methods to solve nonlinear complementarity problems (NCPs) involving P0-function. Several regularization or approximation techniques like Fisher-Burmeister’s method, interior-point methods (IPMs) approaches, or smoothing methods already exist. All the corresponding methods solve a sequence of nonlinear systems of equations and depend on parameters that are difficult to drive to zero. The main novelty of our approach is to consider the smoothing parameters as variables that converge by themselves to zero. We do not need any complicated updating strategy, and then obtain nonparametric algorithms. We prove some global and local convergence results and present several numerical experiments, comparisons, and applications that show the efficiency of our approach.

【 授权许可】

Unknown