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Smoothing Newton and quasi-Newton methods for mixed complementarity problems. (English) Zbl 1168.90623
Summary: 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.

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C53 Methods of quasi-Newton type
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