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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

Corresponding Author:[email protected]

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Bing Tan
University of Electronic Science and Technology of China
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Songxiao Li
University of Electronic Science and Technology of China
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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.
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