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The semismooth Newton method for the solution of quasi-variational inequalities

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  • Francisco Facchinei
  • Christian Kanzow
  • Sebastian Karl
  • Simone Sagratella

Abstract

We consider the application of the globalized semismooth Newton method to the solution of (the KKT conditions of) quasi variational inequalities. We show that the method is globally and locally superlinearly convergent for some important classes of quasi variational inequality problems. We report numerical results to illustrate the practical behavior of the method. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Francisco Facchinei & Christian Kanzow & Sebastian Karl & Simone Sagratella, 2015. "The semismooth Newton method for the solution of quasi-variational inequalities," Computational Optimization and Applications, Springer, vol. 62(1), pages 85-109, September.
  • Handle: RePEc:spr:coopap:v:62:y:2015:i:1:p:85-109
    DOI: 10.1007/s10589-014-9686-4
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    Cited by:

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    3. 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.
    4. Pin-Bo Chen & Gui-Hua Lin & Xide Zhu & Fusheng Bai, 2021. "Smoothing Newton method for nonsmooth second-order cone complementarity problems with application to electric power markets," Journal of Global Optimization, Springer, vol. 80(3), pages 635-659, July.
    5. Tommaso Colombo & Simone Sagratella, 2020. "Distributed algorithms for convex problems with linear coupling constraints," Journal of Global Optimization, Springer, vol. 77(1), pages 53-73, May.
    6. 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.
    7. 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.
    8. Christian Kanzow & Daniel Steck, 2018. "Augmented Lagrangian and exact penalty methods for quasi-variational inequalities," Computational Optimization and Applications, Springer, vol. 69(3), pages 801-824, April.
    9. Lorenzo Lampariello & Christoph Neumann & Jacopo M. Ricci & Simone Sagratella & Oliver Stein, 2020. "An explicit Tikhonov algorithm for nested variational inequalities," Computational Optimization and Applications, Springer, vol. 77(2), pages 335-350, November.
    10. 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.
    11. Leonardo Galli & Christian Kanzow & Marco Sciandrone, 2018. "A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties," Computational Optimization and Applications, Springer, vol. 69(3), pages 629-652, April.
    12. 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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