Characterizations of Strong Regularity for Variational Inequalities over Polyhedral Convex Sets
Asen L. Dontchev, R. TYRRELL ROCKAFELLAR · SIAM Journal on Optimization · 1996
Linear and nonlinear variational inequality problems over a polyhedral convex set are analyzed parametrically. Robinson's notion of strong regularity, as a criterion for the solution set to be a singleton depending Lipschitz continuously on the parameters, is characterized in terms of a new “critical face” condition and in other ways. The consequences for complementarity problems are worked out as a special case. Application is also made to standard nonlinear programming problems with parameters that include the canonical perturbations. In that framework a new characterization of strong regularity is obtained for the variational inequality associated with the Karush–Kuhn–Tucker conditions.