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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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  • M. Lignola & Jacqueline Morgan, 2012. "Approximate values for mathematical programs with variational inequality constraints," Computational Optimization and Applications, Springer, vol. 53(2), pages 485-503, October.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:2:p:485-503
    DOI: 10.1007/s10589-012-9470-2
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    References listed on IDEAS

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    1. S.J. Li & G.Y. Chen & K.L. Teo, 2002. "On the Stability of Generalized Vector Quasivariational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 283-295, May.
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    4. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    5. 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.
    6. 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, January.
    7. M. B. Lignola & J. Morgan, 2007. "On Convergence Results for Weak Efficiency in Vector Optimization Problems with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 117-121, April.
    8. S. Dempe, 1997. "First-Order Necessary Optimality Conditions for General Bilevel Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 95(3), pages 735-739, December.
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    Cited by:

    1. M. Beatrice Lignola & Jacqueline Morgan, 2015. "MinSup Problems with Quasi-equilibrium Constraints and Viscosity Solutions," CSEF Working Papers 393, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    2. Francesco Caruso & M. Beatrice Lignola & Jacqueline Morgan, 2020. "Regularization and Approximation Methods in Stackelberg Games and Bilevel Optimization," Springer Optimization and Its Applications, in: Stephan Dempe & Alain Zemkoho (ed.), Bilevel Optimization, chapter 0, pages 77-138, Springer.
    3. M. Beatrice Lignola & Jacqueline Morgan, 2012. "Approximating Security Values of MinSup Problems with Quasi-variational Inequality Constraints," CSEF Working Papers 321, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 09 Oct 2014.
    4. M. Beatrice Lignola & Jacqueline Morgan, 2013. "Asymptotic Behavior of Regularized OptimizationProblems with Quasi-variational Inequality Constraints," CSEF Working Papers 350, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.

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