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Solving strongly monotone variational and quasi-variational inequalities

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  • NESTEROV, Yu.
  • SCRIMALI, Laura
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    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.

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    File URL: http://alfresco.uclouvain.be/alfresco/download/attach/workspace/SpacesStore/91924c94-197b-4b09-beee-b4567b0eb61f/coredp_2006_107.pdf
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    Bibliographic Info

    Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2006107.

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    Date of creation: 00 Dec 2006
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    Handle: RePEc:cor:louvco:2006107

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    Related research

    Keywords: variational inequality; quasivariational inequality; monotone operators; complexity analysis; efficiency estimate; optimal methods;

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    1. 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.
    2. 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.
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    Cited by:
    1. Frank Lenzen & Florian Becker & Jan Lellmann & Stefania Petra & Christoph Schnörr, 2013. "A class of quasi-variational inequalities for adaptive image denoising and decomposition," Computational Optimization and Applications, Springer, vol. 54(2), pages 371-398, March.
    2. 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.

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