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

✍ Scribed by Sheng-Long Hu; Zheng-Hai Huang; Jein-Shan Chen

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 804 KB
• Volume: 230
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2008.10.056

✦ Synopsis

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 NCPfunctions 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.