Abstract

In this work, we study the multivalued complementarity problem for polyhedral multifunctions under homogeneity assumptions. We employ an approach that consists in approximating the equivalent variational inequality formulation of the problem and studying the asymptotic behavior of sequences of solutions to these approximation problems. To do this, we employ results and the language of Variational Analysis. The novelty of this approach lies in the fact that it allows us to obtain not only existence results but also stability ones. We consider that our results can be used for developing numerical algorithms for solving multivalued complementarity problems. © 2009 Elsevier Ltd. All rights reserved.