Error bound results for generalized D-gap functions of nonsmooth variational inequality problems |
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Authors: | Guoyin Li Chunming Tang |
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Institution: | a Department of Applied Mathematics, The University of New South Wales, Sydney, NSW, Australia b Department of Mathematics and Information Science, Guangxi University, Nanning, Guangxi, PR China |
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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. |
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Keywords: | 65H10 90C26 |
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