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Solving strongly monotone variational and quasi-variational inequalities

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  • NESTEROV, Yu.
  • SCRIMALI, Laura

Abstract

In this paper we develop a new and efficient method for variational inequality with Lipschitz continuous strongly monotone operator. Our analysis is based on a new strongly convex merit function. We apply a variant of the developed scheme for solving quasivariational inequality. As a result, we significantly improve the standard sufficient condition for existence and uniqueness of their solutions. Moreover, we get a new numerical scheme, which rate of convergence is much higher than that of the straightforward gradient method.

Suggested Citation

  • 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).
    • Handle: RePEc:cor:louvco:2006107
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2006.html
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    References listed on IDEAS

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    1. WEI, Jing-Yuan & SMEERS, Yves, 1999. "Spatial oligopolistic electricity models with Cournot generators and regulated transmission prices," LIDAM Reprints CORE 1454, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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, January.
    3. Bliemer, Michiel C. J. & Bovy, Piet H. L., 2003. "Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 37(6), pages 501-519, July.
    4. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
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    Cited by:

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    2. Tran Quoc & Le Muu, 2012. "Iterative methods for solving monotone equilibrium problems via dual gap functions," Computational Optimization and Applications, Springer, vol. 51(2), pages 709-728, March.
    3. Rachana Gupta & Aparna Mehra, 2012. "Gap functions and error bounds for quasi variational inequalities," Journal of Global Optimization, Springer, vol. 53(4), pages 737-748, August.
    4. 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.
    5. 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.
    6. 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.
    7. Nadja Harms & Tim Hoheisel & Christian Kanzow, 2014. "On a Smooth Dual Gap Function for a Class of Quasi-Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 413-438, November.

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