Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems |
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Authors: | Kung Fu Ng Lu Lin Tan |
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Institution: | (1) Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, People’s Republic of China |
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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).
The research of this author was supported by an Earmarked Grant from the Research Council of Hong Kong. |
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Keywords: | Nonsmooth variational inequality problem Merit function Regularized gap function Error bound |
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