Regularization Method for the Variational Inequality Problem over the Set of Solutions to the Generalized Equilibrium Problem

Yanlai Song and Omar Bazighifan
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Yanlai Song: College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China
Omar Bazighifan: Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy

Mathematics, 2022, vol. 10, issue 14, 1-20

Abstract: The paper is devoted to bilevel problems: variational inequality problems over the set of solutions to the generalized equilibrium problems in a Hilbert space. To solve these problems, an iterative algorithm is proposed that combines the ideas of the Tseng’s extragradient method, the inertial idea and iterative regularization. The proposed method adopts a non-monotonic stepsize rule without any line search procedure. Under suitable conditions, the strong convergence of the resulting method is obtained. Several numerical experiments are also provided to illustrate the efficiency of the proposed method with respect to certain existing ones.

Keywords: Hilbert space; monotone operator; Tseng’s extragradient method; regularization method; strong convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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