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- Title
Variational Inequalities over Perturbed Polyhedral Convex Sets.
- Authors
Shu Lu; Robinson, Stephen M.
- Abstract
This paper provides conditions for existence of a locally unique, Lipschitzian solution of a linear variational inequality posed over a polyhedral convex set in ℝn 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 defining 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.
- Subjects
CONVEX sets; LINEAR programming; MATHEMATICAL programming; PERTURBATION theory; LIPSCHITZ spaces; VARIATIONAL inequalities (Mathematics)
- Publication
Mathematics of Operations Research, 2008, Vol 33, Issue 3, p689
- ISSN
0364-765X
- Publication type
Article
- DOI
10.1287/moor.1070.0297