Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems

Authors:
Sheng-Long Hu;Zheng-Hai Huang;Jein-Shan Chen
Affiliations:
Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, PR China;Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, PR China;Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, we propose a new family of NCP-functions and the corresponding merit functions, which are the generalization of some popular NCP-functions and the related merit functions. We show that the new NCP-functions and the corresponding merit functions possess a system of favorite properties. Specially, we show that the new NCP-functions are strongly semismooth, Lipschitz continuous, and continuously differentiable; and that the corresponding merit functions have SC^1 property (i.e., they are continuously differentiable and their gradients are semismooth) and LC^1 property (i.e., they are continuously differentiable and their gradients are Lipschitz continuous) under suitable assumptions. Based on the new NCP-functions and the corresponding merit functions, we investigate a derivative free algorithm for the nonlinear complementarity problem and discuss its global convergence. Some preliminary numerical results are reported.