Variational inequalities over perturbed polyhedral convex sets

• 成果类型: Article
• 署名作者: Lu, Shu; Robinson, Stephen M.
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill; University of Wisconsin System; University of Wisconsin Madison
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1070.0297
• 发表日期: 2008
• 页码: 689-711
• 关键词: lipschitz continuity; normal maps; STABILITY; PROGRAMS; THEOREM; PROOF

摘要

This paper provides conditions for existence of a locally unique, Lipschitzian solution of a linear variational inequality posed over a polyhedral convex set in R-n under perturbation of either or both of the constant term in the variational inequality and the right-hand side of the system of linear constraints de. ning its feasible set. Conditions for perturbation of just the constant term are well known. Here we show that a suitable extension of those conditions suffices for the more general case in which the right-hand side of the constraints varies also. As a consequence, we obtain existence, uniqueness, and Lipschitz continuity properties of solutions of nonlinear variational inequalities posed over perturbed polyhedral convex sets.