DOI: 10.24193/fpt-ro.2022.1.25

Authors: Bing Tan, Adrian Petruşel, Xiaolong Qin and Jen-Chih Yao

Abstract: In this paper, we investigate three new relaxed single projection methods with alternating inertial extrapolation steps and adaptive non-monotonic step sizes for solving pseudo-monotone variational inequalities in real Hilbert spaces. The proposed algorithms need to compute the projection on the feasible set only once in each iteration and they can work adaptively without the prior information of the Lipschitz constant of the mapping. The weak convergence theorems of the proposed iterative schemes are established under some appropriate conditions imposed on the parameters. These methods recover the Fejér monotonicity of the even subsequence with respect to the solution and obtain linear convergence rates. Finally, some numerical experiments and applications to optimal control problems are provided to demonstrate the advantages and efficiency of the proposed methods compared to some recent related ones.

Key Words and Phrases: Variational inequality, alternated inertial method, projection and contraction method, subgradient extragradient method, pseudo-monotone operator, adaptive stepsize.

2010 Mathematics Subject Classification: 47J20, 47J25, 47J30, 47H10, 68W10, 65K15.

Published on-line: February 1st, 2022.

Abstract pdf          Fulltext pdf

Back to volume's table of contents