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Asymptotic analysis, existence and sensitivity resultsfor aclass of multivalued complementarity problems

Published online by Cambridge University Press:  22 March 2006

Fabián Flores-Bazán  and
Rubén López
Fabián Flores-Bazán
Affiliation:
Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Concepción, Chile; [email protected]
Rubén López
Affiliation:
Facultad de Ingeniería, Universidad Católica de la Santísima Concepción, Concepción, Chile; [email protected]
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Abstract

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

Keywords

Multivalued complementarity problemcopositive mappingsasymptotic analysisouter semicontinuitygraphical convergence.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 2 , April 2006 , pp. 271 - 293
Copyright
© EDP Sciences, SMAI, 2006

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