Error bounds of regularized gap functions for nonsmooth variational inequality problems

• 成果类型: Article
• 署名作者: Ng, Kung Fu; Tan, Lu Lin
• 署名单位: Chinese University of Hong Kong
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-006-0007-2
• 发表日期: 2007
• 页码: 405-429
• 关键词: local uniqueness

摘要

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).