Global and global linear convergence of smoothing algorithm for the Cartesian $P_*(\kappa)$-SCLCP

Zheng-Hai Huang; Nan Lu

doi:10.3934/jimo.2012.8.67

Article Contents

2012, Volume 8, Issue 1: 67-86. Doi: 10.3934/jimo.2012.8.67

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Global and global linear convergence of smoothing algorithm for the Cartesian $P_*(\kappa)$-SCLCP

Zheng-Hai Huang^1, and
Nan Lu^2,

1.
Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P.R.
2.
Department of Mathematics, Xidian University, XiAn 710071

Received: September 30, 2010

Revised: June 30, 2011

Published: December 2011

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Abstract

In this paper, we consider the linear complementarity problem over Euclidean Jordan algebras with a Cartesian $P_*(\kappa)$-transformation, which is denoted by the Cartesian $P_*(\kappa)$-SCLCP. A smoothing algorithm is extended to solve the Cartesian $P_*(\kappa)$-SCLCP. We show that the algorithm is globally convergent if the problem concerned has a solution. In particular, we show that the algorithm is globally linearly convergent under a weak assumption.

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Mathematics Subject Classification: Primary: 90C22, 90C25; Secondary: 90C33.

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