Strong Convergent Theorems Governed by Pseudo-Monotone Mappings

Liya Liu, Xiaolong Qin and Jen-Chih Yao
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Liya Liu: School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China
Xiaolong Qin: Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Jen-Chih Yao: Center for General Education, China Medical University, Taichung 40447, Taiwan

Mathematics, 2020, vol. 8, issue 8, 1-15

Abstract: The purpose of this paper is to introduce two different kinds of iterative algorithms with inertial effects for solving variational inequalities. The iterative processes are based on the extragradient method, the Mann-type method and the viscosity method. Convergence theorems of strong convergence are established in Hilbert spaces under mild assumption that the associated mapping is Lipschitz continuous, pseudo-monotone and sequentially weakly continuous. Numerical experiments are performed to illustrate the behaviors of our proposed methods, as well as comparing them with the existing one in literature.

Keywords: variational inequality; inertial extrapolation; pseudomonotonicity; projection method; extragradient method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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