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Using the Banach Contraction Principle to Implement the Proximal Point Method for Multivalued Monotone Variational Inequalities

Journal of Optimization Theory and Applications volume 124, pages 285–306 (2005)Cite this article

Abstract

We apply the Banach contraction-mapping fixed-point principle for solving multivalued strongly monotone variational inequalities. Then, we couple this algorithm with the proximal-point method for solving monotone multivalued variational inequalities. We prove the convergence rate of this algorithm and report some computational results.

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Author information

Authors and Affiliations

  1. Post and Telecommunications Institute of Technology, Hanoi, Vietnam

    P. N. Anh

  2. Institute of Mathematics, Hanoi, Vietnam

    L. D. Muu

  3. Unité d’Optimisation, Département de Mathématique, Facultés Universitaires Notre Dame de la Paix, Namur, Belgium

    V. H. Nguyen

  4. Unité d’Optimisation, Département de Mathématique, Facultés Universitaires Notre Dame de la Paix, Namur, Belgium

    J. J. Strodiot

Authors
  1. P. N. Anh
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  2. L. D. Muu
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  3. V. H. Nguyen
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  4. J. J. Strodiot
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Additional information

This work was completed during the stay of the second author at the Department of Mathematics, University of Namur, Namur, Belgium, 2003.

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Anh, P.N., Muu, L.D., Nguyen, V.H. et al. Using the Banach Contraction Principle to Implement the Proximal Point Method for Multivalued Monotone Variational Inequalities. J Optim Theory Appl 124, 285–306 (2005). https://doi.org/10.1007/s10957-004-0926-0

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  • DOI: https://doi.org/10.1007/s10957-004-0926-0

Keywords

  • Multivalued monotone variational inequalities
  • proximal-point algorithms
  • Banach contraction-mapping fixed-point methods
  • convergence rates