Two New Modified Regularized Methods for Solving the Variational Inclusion and Null Point Problems

Yuanheng Wang (), Miaoqing Li, Chengru Yao and Bingnan Jiang
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Yuanheng Wang: College of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Miaoqing Li: College of Mathematics, Zhejiang Normal University, Jinhua 321004, China
Chengru Yao: Xichuan County Education and Sports Bureau of Henan Province, Nanyang 474450, China
Bingnan Jiang: College of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Mathematics, 2023, vol. 11, issue 6, 1-21

Abstract: In this article, based on the regularization techniques, we construct two new algorithms combining the forward-backward splitting algorithm and the proximal contraction algorithm, respectively. Iterative sequences of the new algorithms can converge strongly to a common solution of the variational inclusion and null point problems in real Hilbert spaces. Multi-inertial extrapolation steps are applied to expedite their convergence rate. We also give some numerical experiments to certify that our algorithms are viable and efficient.

Keywords: variational inclusion; null point; regularized method; multi-step inertial iteration; strong convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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