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

Authors:
Guoyin Li;Chunming Tang;Zengxin Wei
Affiliations:
Department of Applied Mathematics, The University of New South Wales, Sydney, NSW, Australia;Department of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, PR China;Department of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

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.