Smoothing Newton and Quasi-Newton Methods for Mixed Complementarity Problems |
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Authors: | Donghui Li Masao Fukushima |
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Affiliation: | (1) Department of Applied Mathematics, Hunan University, Changsha, 410082, China;(2) Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan |
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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. |
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Keywords: | mixed complementarity problem smoothing function Newton's method quasi-Newton method |
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