## Characterizations of strong regularity for variational inequalities over polyhedral convex sets (1996)

Venue: | SIAM J. OPTIMIZATION |

Citations: | 46 - 15 self |

### BibTeX

@ARTICLE{Dontchev96characterizationsof,

author = {A. L. Dontchev and R. T. Rockafellar},

title = { Characterizations of strong regularity for variational inequalities over polyhedral convex sets},

journal = {SIAM J. OPTIMIZATION},

year = {1996},

pages = {1087--1105}

}

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### OpenURL

### Abstract

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.