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Volume 5, Issue 3, 1 December 2023, Pages 399-418
Abstract. In this paper, we propose an inertial shrinking Tseng’s extragradient algorithm with a self-adaptive step size for solving pseudomonotone variational inequality problem with non-Lipschitz operators in the framework of 2-uniformly convex Banach spaces which are also uniformly smooth. Moreover, we prove a strong convergence result for the proposed algorithm under mild conditions on the control parameters. The main advantages of our algorithm are: our proposed algorithm solves the variational inequality problem with a larger class of mappings (pseudomonotone and non-Lipschitz operators); unlike the existing results in the literature, our algorithm does not require any linesearch technique even while the operator is non-Lipschitz; minimized number of projections per iteration compared to related results in the literature; and the inertial technique employed which speeds up the rate of convergence. Finally, we present some numerical examples to illustrate the efficiency of our algorithm in comparison with related methods in the literature.
How to Cite this Article:
O.T. Mewomo, A.O.E. Owolabi, T.O. Alakoya, Self-adaptive inertial shrinking Tseng’s extragradient method for solving a pseudomonotone variational inequalities in Banach spaces, J. Appl. Numer. Optim. 5 (2023), 399-418.