Journal of Optimization Theory and Applications

, Volume 124, Issue 2, pp 285–306 | Cite as

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

  • P. N. Anh
  • L. D. Muu
  • V. H. Nguyen
  • J. J. Strodiot


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.


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


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • P. N. Anh
    • 1
  • L. D. Muu
    • 2
  • V. H. Nguyen
    • 3
  • J. J. Strodiot
    • 4
  1. 1.Post and Telecommunications Institute of TechnologyHanoiVietnam
  2. 2.Institute of MathematicsHanoiVietnam
  3. 3. Unité d’Optimisation, Département de MathématiqueFacultés Universitaires Notre Dame de la PaixNamurBelgium
  4. 4. Unité d’Optimisation, Département de MathématiqueFacultés Universitaires Notre Dame de la PaixNamurBelgium

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