Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems

Authors:
Kung Fu Ng;Lu Lin Tan
Affiliations:
The Chinese University of Hong Kong, Department of Mathematics, Hong Kong, People’s Republic of China;The Chinese University of Hong Kong, Department of Mathematics, Hong Kong, People’s Republic of China
Venue:
Mathematical Programming: Series A and B
Year:
2007

Citing 0
Cited 2

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

Journal of Computational and Applied Mathematics
Gap functions and global error bounds for set-valued variational inequalities

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the Clarke–Rockafellar directional derivatives of the regularized gap functions (and of some modified ones) for the variational inequality problem (VIP) defined by a locally Lipschitz but not necessarily differentiable function on a closed convex set in an Euclidean space. As applications we show that, under the strong monotonicity assumption, the regularized gap functions have fractional exponent error bounds and consequently that the sequences provided by an algorithm of Armijo type converge to the solution of the (VIP).