Quadratic one-step smoothing Newton method for P0-LCP without strict complementarity

Authors:
Liping Zhang;Ziyou Gao
Affiliations:
Institute of System Sciences, School of Traffic and Transportation, Northern Jiaotong University, Beijing 100044, China;Institute of System Sciences, School of Traffic and Transportation, Northern Jiaotong University, Beijing 100044, China
Venue:
Applied Mathematics and Computation
Year:
2003

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Abstract

In this paper we propose a modified one-step smoothing Newton method for solving the P0 linear complementarity problem (P0-LCP) based on Kanzow's smoothing function. Our smoothing Newton method solves only one linear system of equations and performs only one line search at each iteration. It is proved that our proposed algorithm has global convergence and local quadratic convergence in absence of strict complementarity assumption at the P0-LCP solution. Under weaker conditions, our convergence results are much stronger than many previous literatures.