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

Zheng-Hai Huang; Shang-Wen Xu

doi:10.3934/jimo.2007.3.569

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2007, Volume 3, Issue 3: 569-584. Doi: 10.3934/jimo.2007.3.569

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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
2.
Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P.R.

Received: September 2006

Revised: April 2007

Published: July 2007

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Abstract

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,
non-interior-point smoothing algorithm,
maximally complementarity solution.

Mathematics Subject Classification: Primary: 90C33; Secondary: 65K10.

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