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Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces

Abstract

In this paper, we introduce an inertial projection-type method with different updating strategies for solving quasi-variational inequalities with strongly monotone and Lipschitz continuous operators in real Hilbert spaces. Under standard assumptions, we establish different strong convergence results for the proposed algorithm. Primary numerical experiments demonstrate the potential applicability of our scheme compared with some related methods in the literature.

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Acknowledgements

We are grateful to the anonymous referees and editor whose insightful comments helped to considerably improve an earlier version of this paper. The research of the first author is supported by an ERC Grant from the Institute of Science and Technology (IST).

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Correspondence to Aviv Gibali.

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Shehu, Y., Gibali, A. & Sagratella, S. Inertial Projection-Type Methods for Solving Quasi-Variational Inequalities in Real Hilbert Spaces. J Optim Theory Appl 184, 877–894 (2020). https://doi.org/10.1007/s10957-019-01616-6

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Keywords

  • Quasi-variational inequalities
  • Inertial extrapolation step
  • Strong monotonicity
  • Hilbert spaces

Mathematics Subject Classification

  • 47H05
  • 47J20
  • 47J25
  • 65K15
  • 90C25