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Approximate values for mathematical programs with variational inequality constraints

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  • M. Lignola

    ()

  • Jacqueline Morgan

    ()

Abstract

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. Copyright Springer Science+Business Media, LLC 2012

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File URL: http://hdl.handle.net/10.1007/s10589-012-9470-2
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Bibliographic Info

Article provided by Springer in its journal Computational Optimization and Applications.

Volume (Year): 53 (2012)
Issue (Month): 2 (October)
Pages: 485-503

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Handle: RePEc:spr:coopap:v:53:y:2012:i:2:p:485-503

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Web page: http://www.springer.com/math/journal/10589

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Related research

Keywords: Mathematical program; Bilevel problem; Variational inequality; Infimal value; Approximate solution; Perturbation;

References

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  1. Laurent Drouet & Alain Haurie & Francesco Moresino & Jean-Philippe Vial & Marc Vielle & Laurent Viguier, 2008. "An oracle based method to compute a coupled equilibrium in a model of international climate policy," Computational Management Science, Springer, vol. 5(1), pages 119-140, February.
  2. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, 01.
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Cited by:
  1. M. Beatrice Lignola & Jacqueline Morgan, 2013. "Asymptotic Behavior of Regularized OptimizationProblems with Quasi-variational Inequality Constraints," CSEF Working Papers, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy 350, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
  2. M. Beatrice Lignola & Jacqueline Morgan, 2012. "Approximating Values of MinSup Problems with Quasi-variational Inequality Constraints," CSEF Working Papers, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy 321, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 27 Nov 2012.

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