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Ferdinard U. Ogbuisi, Yekini Shehu, A new inertial relaxed Tseng extrgradient method for solving quasi-monotone bilevel variational inequality problems in Hilbert spaces

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DOI: 10.23952/jnva.7.2023.3.09

Volume 7, Issue 3, 1 June 2023, Pages 449-464

 

Abstract. In this paper, we introduce an inertial relaxed Tseng extragradient method involving only a single projection for solving bilevel variational inequality problems with Lipschitz continuous and quasimonotone mapping in Hilbert spaces. Under some mild standard assumptions, we obtain a strong convergence result for solving bilevel quasimonotone variational inequality problems. The main advantages of the proposed iterative method are that it requires only one projection onto the feasible set and the use self adaptive step-size rule based on operator knowledge rather than a Lipschitz constant or some line search method. Moreover, some interesting preliminary numerical experiments and comparisons were presented.

 

How to Cite this Article:
F.U. Ogbuisi, Y. Shehu, A new inertial relaxed Tseng extrgradient method for solving quasi-monotone bilevel variational inequality problems in Hilbert spaces, J. Nonlinear Var. Anal. 7 (2023), 449-464.