Solution Continuity in Monotone Affine Variational Inequalities

Authors:
Stephen M. Robinson
Affiliations:
-
Venue:
SIAM Journal on Optimization
Year:
2007

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Abstract

In this paper we study the behavior of solutions of finite-dimensional monotone affine variational inequalities posed over graph-convex polyhedral multifunctions. We identify precisely the class of positive semidefinite linear transformations appearing in these variational inequalities for which the solution sets will be Lipschitzian in the argument of the underlying multifunction. This class is that of cocoercive linear transformations, which include, but are not limited to, those appearing in problems of linear or of convex quadratic programming.