Journal of Global Optimization

, Volume 61, Issue 1, pp 193–202 | Cite as

A hybrid method without extrapolation step for solving variational inequality problems

  • Yu. V. Malitsky
  • V. V. Semenov


In this paper, we introduce a new method for solving variational inequality problems with monotone and Lipschitz-continuous mapping in Hilbert space. The iterative process is based on well-known projection method and the hybrid (or outer approximation) method. However we do not use an extrapolation step in the projection method. The absence of one projection in our method is explained by slightly different choice of sets in the hybrid method. We prove a strong convergence of the sequences generated by our method.


Variational inequality Monotone mapping Hybrid method Projection method Strong convergence 

Mathematics Subject Classification




The authors would like to extend their gratitude towards anonymous referees whose constructive suggestions helped us to improve the presentation of this paper.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of CyberneticsTaras Shevchenko National University of KyivKievUkraine

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