Smoothing Newton and Quasi-Newton Methods for Mixed Complementarity Problems

Authors:
Donghui Li;Masao Fukushima
Affiliations:
Department of Applied Mathematics, Hunan University, Changsha 410082, China. dhli@mail.hunu.edu.cn;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan. fuku@i.kyoto-u.ac.jp
Venue:
Computational Optimization and Applications
Year:
2000

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Abstract

The mixed complementarity problem can be reformulated as a nonsmooth equation by using the median operator. In this paper, we first study some useful properties of this reformulation and then derive the Chen-Harker-Kanzow-Smale smoothing function for the mixed complementarity problem. On the basis of this smoothing function, we present a smoothing Newton method for solving the mixed complementarity problem. Under suitable conditions, the method exhibits global and quadratic convergence properties. We also present a smoothing Broyden-like method based on the same smoothing function. Under appropriate conditions, the method converges globally and superlinearly.