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Abdellah Bnouhachem, An inertial extragradient algorithm with non-monotone step sizes for variational inequality problems and fixed point problems of nonexpansive semigroups

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DOI: 10.23952/jano.7.2025.2.08
Volume 7, Issue 2, 1 August 2025, Pages 275-288

 

Abstract. In this paper, we propose an inertial extragradient algorithm with non-monotone step sizes for approximating a common solution of a variational inequality problem of pseudomonotone and uniformly continuous operators and a fixed point problem of nonexpansive semigroups in the setting of real Hilbert spaces. By utilizing a self-adaptive technique that produces non-monotonic step sizes, our method ensures strong convergence without requiring Armijo-type line searches. Finally, to assess the performance of the proposed algorithm, we provide some numerical results.

 

How to Cite this Article:
A. Bnouhachem, An inertial extragradient algorithm with non-monotone step sizes for variational inequality problems and fixed point problems of nonexpansive semigroups, J. Appl. Numer. Optim. 7 (2025), 275-288.