Smoothing Newton methods for symmetric cone linear complementarity problem with the Cartesian $P$/$P_0$-property

Li-Xia Liu; Sanyang  Liu; Chun-Feng Wang

doi:10.3934/jimo.2011.7.53

Article Contents

2011, Volume 7, Issue 1: 53-66. Doi: 10.3934/jimo.2011.7.53

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Smoothing Newton methods for symmetric cone linear complementarity problem with the Cartesian $P$/$P_0$-property

1.
Department of Applied Mathematics, Xidian University, Xi'an 710071
2.
Department of Applied Mathematics, Xidian University, Xi'an, 710071
3.
College of Mathematics and Information, Henan Normal University, Xinxiang 453007

Received: March 31, 2010

Revised: August 31, 2010

Published: December 2010

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Abstract

A smoothing Newton method based on the CHKS smoothing function for a class of non-monotone symmetric cone linear complementarity problem (SCLCP) with the Cartesian $P$-property and a regularization smoothing Newton method for SCLCP with the Cartesian $P_0$-property are proposed. The existence of Newton directions and the boundedness of iterates, two important theoretical issues encountered in the smoothing method, are showed for these two classes of non-monotone SCLCP. Finally, we show that these two algorithms are globally convergent. Moreover, they are globally linear and locally quadratic convergent under a nonsingular assumption.

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

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