American Institute of Mathematical Sciences

Advanced
July  2007, 3(3): 569-584. doi: 10.3934/jimo.2007.3.569

Convergence properties of a non-interior-point smoothing algorithm for the P*NCP

Zheng-Hai Huang 1, and  Shang-Wen Xu 2,

1. 

Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China
2. 

Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P.R., China

Received  September 2006 Revised  April 2007 Published  July 2007

In this paper, a non-interior-point smoothing algorithm is applied to solve the $P_*$ nonlinear complementarity problem (NCP). The algorithm is proved to be globally convergent under an assumption that the $P_*$ NCP has a nonempty solution set. In particular, the solution obtained by the algorithm is shown to be a maximally complementary solution of the $P_*$ NCP. The results we obtained strictly generalize the relative results appeared in the literature.
Keywords: $P_*$ nonlinear complementarity problem, maximally complementarity solution., non-interior-point smoothing algorithm.
Mathematics Subject Classification: Primary: 90C33; Secondary: 65K1.
Citation: Zheng-Hai Huang, Shang-Wen Xu. Convergence properties of a non-interior-point smoothing algorithm for the P*NCP. Journal of Industrial and Management Optimization, 2007, 3 (3) : 569-584. doi: 10.3934/jimo.2007.3.569
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