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

Fabián Flores-Bazán; Rubén López

ESAIM: Control, Optimisation and Calculus of Variations (2006)

  • Volume: 12, Issue: 2, page 271-293
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Flores-Bazán, Fabián, and López, Rubén. "Asymptotic analysis, existence and sensitivity results for a class of multivalued complementarity problems." ESAIM: Control, Optimisation and Calculus of Variations 12.2 (2006): 271-293. <http://eudml.org/doc/249671>.

@article{Flores2006,
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. },
author = {Flores-Bazán, Fabián, López, Rubén},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Multivalued complementarity problem; copositive mappings; asymptotic analysis; outer semicontinuity; graphical convergence. ; multivalued complementarity problem; asymptotic analysis; outer semicontinuity; graphical convergence},
language = {eng},
month = {3},
number = {2},
pages = {271-293},
publisher = {EDP Sciences},
title = {Asymptotic analysis, existence and sensitivity results for a class of multivalued complementarity problems},
url = {http://eudml.org/doc/249671},
volume = {12},
year = {2006},
}

TY - JOUR
AU - Flores-Bazán, Fabián
AU - López, Rubén
TI - Asymptotic analysis, existence and sensitivity results for a class of multivalued complementarity problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2006/3//
PB - EDP Sciences
VL - 12
IS - 2
SP - 271
EP - 293
AB - 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.
LA - eng
KW - Multivalued complementarity problem; copositive mappings; asymptotic analysis; outer semicontinuity; graphical convergence. ; multivalued complementarity problem; asymptotic analysis; outer semicontinuity; graphical convergence
UR - http://eudml.org/doc/249671
ER -

References

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