Computational Optimization and Applications

, Volume 53, Issue 2, pp 485–503 | Cite as

Approximate values for mathematical programs with variational inequality constraints

  • M. Beatrice Lignola
  • Jacqueline Morgan


In general the infimal value of a mathematical program with variational inequality constraints (MPVI) is not stable under perturbations in the sense that the sequence of infimal values for the perturbed programs may not converge to the infimal value of the original problem even in presence of nice data. Thus, for these programs we consider different types of values which approximate the exact value from below or/and from above under or without perturbations.


Mathematical program Bilevel problem Variational inequality Infimal value Approximate solution Perturbation 



The authors thanks the Referees and the Editor in charge for their stimulating suggestions that helped to improve the paper.


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© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Applicazioni R. CaccioppoliUniversità di Napoli Federico IINapoliItaly
  2. 2.Dipartimento di Matematica e Statistica & CSEFUniversità di Napoli Federico IINapoliItaly

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