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Adaptive hybrid steepest descent algorithms involving an inertial extrapolation term for split monotone variational inclusion problems
  • Zheng Zhou,
  • Bing Tan,
  • Songxiao Li
Zheng Zhou
University of Electronic Science and Technology of China
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Bing Tan
University of Electronic Science and Technology of China
Author Profile
Songxiao Li
University of Electronic Science and Technology of China
Author Profile

Abstract

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.

Peer review status:UNDER REVIEW

27 May 2021Submitted to Mathematical Methods in the Applied Sciences
27 May 2021Assigned to Editor
27 May 2021Submission Checks Completed
28 May 2021Reviewer(s) Assigned