Error bound results for generalized D-gap functions of nonsmooth variational inequality problems

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• 作者：Guoyin Li ; Chunming Tang ; Zengxin Wei
• 关键词：Nonsmooth variational inequality problem ; Free boundary problem ; Generalized D-gap function ; Error bound
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2010
• 出版时间：1 April 2010
• 年：2010
• 卷：233
• 期：11
• 页码：2795-2806
• 全文大小：698 K

文摘

Solving a variational inequality problem can be equivalently reformulated into solving a unconstraint optimization problem where the corresponding objective function is called a merit function. An important class of merit function is the generalized D-gap function introduced in [N. Yamashita, K. Taji, M. Fukushima, Unconstrained optimization reformulations of variational inequality problems, J. Optim. Theory Appl. 92 (1997) 439–456] and Yamashita and Fukushima (1997) [17]. In this paper, we present new fractional local/global error bound results for the generalized D-gap functions of nonsmooth variational inequality problems, which gives an effective estimate on the distance between a specific point to the solution set, in terms of the corresponding function value of the generalized D-gap function. Numerical examples and a simple application to the free boundary problem are also presented to illustrate the significance of our error bound results.