A New Inertial Self-adaptive Gradient Algorithm for the Split Feasibility Problem and an Application to the Sparse Recovery Problem
- Authors
- Vinh, Nguyen The; Hoai, Pham Thi; Dung, Le Anh; Cho, Yeol Je
- Issue Date
- Dec-2023
- Publisher
- Springer Verlag
- Keywords
- 47H04; 47H10; 49J40; CQ algorithm; Hilbert space; sparse recovery problem; Split feasibility problem
- Citation
- Acta Mathematica Sinica, English Series, v.39, no.12, pp 2489 - 2506
- Pages
- 18
- Indexed
- SCIE
SCOPUS
- Journal Title
- Acta Mathematica Sinica, English Series
- Volume
- 39
- Number
- 12
- Start Page
- 2489
- End Page
- 2506
- URI
- https://scholarworks.gnu.ac.kr/handle/sw.gnu/68947
- DOI
- 10.1007/s10114-023-2311-7
- ISSN
- 1439-8516
1439-7617
- Abstract
- In this paper, by combining the inertial technique and the gradient descent method with Polyak’s stepsizes, we propose a novel inertial self-adaptive gradient algorithm to solve the split feasibility problem in Hilbert spaces and prove some strong and weak convergence theorems of our method under standard assumptions. We examine the performance of our method on the sparse recovery problem beside an example in an infinite dimensional Hilbert space with synthetic data and give some numerical results to show the potential applicability of the proposed method and comparisons with related methods emphasize it further. © 2023, Springer-Verlag GmbH Germany & The Editorial Office of AMS.
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