Strong Convergence Theorems for Solving Variational Inequality Problems with Pseudo-monotone and Non-Lipschitz Operators

Gang Cai (), Qiao-Li Dong () and Yu Peng ()
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Gang Cai: Chongqing Normal University
Qiao-Li Dong: Civil Aviation University of China
Yu Peng: Civil Aviation University of China

Journal of Optimization Theory and Applications, 2021, vol. 188, issue 2, No 8, 447-472

Abstract: Abstract In this paper, we propose a new viscosity extragradient algorithm for solving variational inequality problems of pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. We prove a strong convergence theorem under some appropriate conditions imposed on the parameters. Finally, we give some numerical experiments to illustrate the advantages of our proposed algorithms. The main results obtained in this paper extend and improve some related works in the literature.

Keywords: Extragradient method; Variational inequality; Viscosity method; Strong convergence; 65Y05; 47H10; 47H05; 65K15 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-020-01792-w

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