Smoothing Newton method for NCP with the identification of degenerate indices

Authors:
Haodong Yu;Dingguo Pu
Affiliations:
Department of Mathematics, Tongji University, Shanghai, 200092, PR China;Department of Mathematics, Tongji University, Shanghai, 200092, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

We present a new smoothing Newton method for nonlinear complementarity problems (NCP(F)) by using an NCP function to reformulate the problem to its equivalent form. Compared with most current smoothing methods, our method contains an estimating technique based on the active-set strategy. This technique focuses on the identification of the degenerate set for a solution x^* of the NCP(F). The proposed method has the global convergence, each accumulation point is a solution of the problem. The introduction of the active-set strategy effectively reduces the scale of the problem. Under some regularity assumption, the degenerate set can be identified correctly near the solution and local superlinear convergence is obtained as well.