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

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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.

MSC

65H10
90C26

Keywords

Nonsmooth variational inequality problem
Free boundary problem
Generalized D-gap function
Error bound

Cited by (0)

Research of this work is supported by the Chinese NSF grants 10161002 and Guangxi NSF grants 0542043.