Document Type

Technical Report


This paper concerns the study of solution maps to parameterized variational inequalities over generalized polyhedra in reflexive Banach spaces. It has been recognized that generalized polyhedral sets are significantly different from the usual convex polyhedra in infinite dimensions and play an important role in various applications to optimization, particularly to generalized linear programming. Our main goal is to fully characterize robust Lipschitzian stability of the aforementioned solutions maps entirely via their initial data. This is done on the base of the coderivative criterion in variational analysis via efficient calculations of the coderivative and related objects for the systems under consideration. The case of generalized polyhedra is essentially more involved in comparison with usual convex polyhedral sets and requires developing elaborated techniques and new proofs of variational analysis.

Number in Series



Applied Mathematics | Mathematics


This research was partially supported by the US National Science Foundation under grants DMS-0603846 and DMS-1007132 and by the Australian Research Council under grant DP-12092508; and by the Distinguished Young Scholar Foundation of Heilongjiang Province of China (JC200707).