Asymptotic analysis, existence and sensitivity results for a class of multivalued complementarity problems

¹ Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción, Chile; fflores@ing-mat.udec.cl
² Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Concepción, Chile; rlopez@ucsc.cl

Received: 7 October 2004
Revised: 7 March 2005

Abstract

In this work we study the multivalued complementarity problem on the non-negative orthant. This is carried out by describing the asymptotic behavior of the sequence of approximate solutions to its multivalued variational inequality formulation. By introducing new classes of multifunctions we provide several existence (possibly allowing unbounded solution set), stability as well as sensitivity results which extend and generalize most of the existing ones in the literature. We also present some kind of robustness results regarding existence of solution with respect to certain perturbations. Topological properties of the solution-set multifunction are established and some notions of approximable multifunctions are also discussed. In addition, some estimates for the solution set and its asymptotic cone are derived, as well as the existence of solutions for perturbed problems is studied.