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O. T. Mewomo, R. N. Nwokoye, T. O. Alakoyo, G. N. Ogwo, On fixed point iterative methods for solving non-Lipschitz quasi-monotone variational inequalities

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DOI: 10.23952/jano.6.2024.3.08
Volume 6, Issue 3, 1 December 2024, Pages 429-446

 

Abstract. In this paper, we mainly study a class of non-Lipschitz quasi-monotone variational inequalities. We introduce a new inertial algorithm with self-adaptive step sizes for finding the minimum-norm solutions of the variational inequalities. Unlike the existing results on non-Lipschitz variational inequalities, our algorithm does not require any linesearch technique. We prove that the sequence generated by our proposed algorithm converges strongly to the minimum-norm solutions of the variational inequalities in Hilbert spaces. In addition, we also consider a class of non-Lipschitz variational inequalities without monotonicity. Finally, we present several numerical examples to illustrate our algorithm by comparing it with some existing methods.

 

How to Cite this Article:
O. T. Mewomo, R. N. Nwokoye, T. O. Alakoyo, G. N. Ogwo, On fixed point iterative methods for solving non-Lipschitz quasi-monotone variational inequalities, J. Appl. Numer. Optim. 6 (2024), 429-446.