Relaxed Single Projection Methods for Solving Bilevel Variational Inequality Problems in Hilbert Spaces

Ferdinard U. Ogbuisi (), Yekini Shehu () and Jen-Chih Yao ()
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Ferdinard U. Ogbuisi: University of Nigeria
Yekini Shehu: Zhejiang Normal University
Jen-Chih Yao: China Medical University Hospital, China Medical University

Networks and Spatial Economics, 2023, vol. 23, issue 3, No 6, 678 pages

Abstract: Abstract In this paper, we first propose a relaxed regularization projection method involving only a single projection for solving monotone bilevel variational inequality problem in Hilbert spaces and secondly we give an alternated inertial version of the first algorithm. The two proposed algorithms involve self adaptive step-sizes and the algorithms can easily be implemented without the prior knowledge of Lipschitz and strongly monotone constants of operators. Under some mild standard assumptions, we obtain the strong convergence of the two algorithms to the unique solution of the bilevel equilibrium problem. Moreover, some interesting numerical experiments are given to demonstrate the applicability of the results and also to compare with existing algorithms.

Keywords: Alternated inertial; Bilevel variational inequality problem; Monotone operator; Projection method; Hilbert spaces; 49J53; 65K10; 49M37; 90C25 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11067-023-09594-z

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