Two Regularization Methods for the Variational Inequality Problem over the Set of Solutions of the Generalized Mixed 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 16, 1-20

Abstract: In this work, we consider bilevel problems: variational inequality problems over the set of solutions of the generalized mixed equilibrium problems. Two new inertial extragradient methods are proposed for solving these problems. Under appropriate conditions, we prove strong convergence theorems for the proposed methods by the regularization technique. Finally, some numerical examples are provided to show the efficiency of the proposed algorithms.

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

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