Optimization Letters

, Volume 13, Issue 8, pp 1885–1896 | Cite as

Gradient-type projection methods for quasi-variational inequalities

  • Nevena MijajlovićEmail author
  • Milojica Jaćimović
  • Muhammad Aslam Noor
Original Paper


We study methods for solving quasi-variational inequalities which are a notable generalization of the variational inequalities. Solving quasi-variational inequality requires that the corresponding variational inequality be solved concurrently with the calculation of a fixed point of the set-valued mapping. For this reason, the literature on quasi-variational inequalities is not very extensive in what concerns solution methods. In this paper we suggest and analyze a new continuous and iterative variants of some generalizations of the gradient-type projection method for solving quasi-variational inequalities. Using the technique of Noor, we also propose a new two-step iterative scheme. We also establish sufficient conditions for the convergence of the proposed methods and estimate the rates of convergence.


Quasi-variational inequalities Continuous and iterative methods Gradient-type projection method Convergence 



We are very grateful to the referees for their valuable comments on the paper.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Nevena Mijajlović
    • 1
    Email author
  • Milojica Jaćimović
    • 1
  • Muhammad Aslam Noor
    • 2
  1. 1.Department of MathematicsUniversity of MontenegroPodgoricaMontenegro
  2. 2.Department of MathematicsCOMSATS University IslamabadIslamabadPakistan

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