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A canonical duality approach for the solution of affine quasi-variational inequalities

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  • Vittorio Latorre
  • Simone Sagratella

Abstract

We propose a new formulation of the Karush–Kunt–Tucker conditions of a particular class of quasi-variational inequalities. In order to reformulate the problem we use the Fisher–Burmeister complementarity function and canonical duality theory. We establish the conditions for a critical point of the new formulation to be a solution of the original quasi-variational inequality showing the potentiality of such approach in solving this class of problems. We test the obtained theoretical results with a simple heuristic that is demonstrated on several problems coming from the academy and various engineering applications. Copyright Springer Science+Business Media New York 2016

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  • Vittorio Latorre & Simone Sagratella, 2016. "A canonical duality approach for the solution of affine quasi-variational inequalities," Journal of Global Optimization, Springer, vol. 64(3), pages 433-449, March.
    • Handle: RePEc:spr:jglopt:v:64:y:2016:i:3:p:433-449
    DOI: 10.1007/s10898-014-0236-5
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    References listed on IDEAS

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    4. NESTEROV, Yu. & SCRIMALI, Laura, 2006. "Solving strongly monotone variational and quasi-variational inequalities," LIDAM Discussion Papers CORE 2006107, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    6. D. Aussel & R. Correa & M. Marechal, 2011. "Gap Functions for Quasivariational Inequalities and Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 474-488, December.
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    Cited by:

    1. Axel Dreves & Simone Sagratella, 2020. "Nonsingularity and Stationarity Results for Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 711-743, June.
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    3. Yekini Shehu & Aviv Gibali & Simone Sagratella, 2020. "Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 877-894, March.
    4. Didier Aussel & Simone Sagratella, 2017. "Sufficient conditions to compute any solution of a quasivariational inequality via a variational inequality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 3-18, February.
    5. Lampariello, Lorenzo & Neumann, Christoph & Ricci, Jacopo M. & Sagratella, Simone & Stein, Oliver, 2021. "Equilibrium selection for multi-portfolio optimization," European Journal of Operational Research, Elsevier, vol. 295(1), pages 363-373.
    6. Lorenzo Lampariello & Simone Sagratella, 2020. "Numerically tractable optimistic bilevel problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 277-303, June.

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