Adaptive hybrid steepest descent algorithms involving an inertial
extrapolation term for split monotone variational inclusion problems
- Zheng Zhou,
- Bing Tan,
- Songxiao Li
Bing Tan
University of Electronic Science and Technology of China
Author ProfileSongxiao Li
University of Electronic Science and Technology of China
Author ProfileAbstract
In this paper, we discuss the split monotone variational inclusion
problem and propose two new inertial algorithms in infinite-dimensional
Hilbert spaces. As well as, the iterative sequence by the proposed
algorithms converges strongly to the solution of a certain variational
inequality with the help of the hybrid steepest descent method.
Furthermore, an adaptive step size criterion is considered in suggested
algorithms to avoid the difficulty of calculating the operator norm.
Finally, some numerical experiments show that our algorithms are
realistic and summarize the known results.27 May 2021Submitted to Mathematical Methods in the Applied Sciences 27 May 2021Submission Checks Completed
27 May 2021Assigned to Editor
28 May 2021Reviewer(s) Assigned
22 Sep 2021Review(s) Completed, Editorial Evaluation Pending
23 Sep 2021Editorial Decision: Revise Major
30 Sep 20211st Revision Received
30 Sep 2021Submission Checks Completed
30 Sep 2021Assigned to Editor
02 Oct 2021Reviewer(s) Assigned
02 Oct 2021Review(s) Completed, Editorial Evaluation Pending
03 Oct 2021Editorial Decision: Accept
Oct 2022Published in Mathematical Methods in the Applied Sciences volume 45 issue 15 on pages 8835-8853. 10.1002/mma.7931