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Gradient-type projection methods for quasi-variational inequalities

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Abstract

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.

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Acknowledgements

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

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Authors and Affiliations

  1. Department of Mathematics, University of Montenegro, Dzordza Vasingtona bb, 81000, Podgorica, Montenegro

    Nevena Mijajlović & Milojica Jaćimović

  2. Department of Mathematics, COMSATS University Islamabad, Park Road, Islamabad, Pakistan

    Muhammad Aslam Noor

Authors
  1. Nevena Mijajlović
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  2. Milojica Jaćimović
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  3. Muhammad Aslam Noor
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Correspondence to Nevena Mijajlović.

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Mijajlović, N., Jaćimović, M. & Noor, M.A. Gradient-type projection methods for quasi-variational inequalities. Optim Lett 13, 1885–1896 (2019). https://doi.org/10.1007/s11590-018-1323-1

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  • DOI: https://doi.org/10.1007/s11590-018-1323-1

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