Abstract
We study a certain class of split inverse problems which includes many other split-type problems. We propose a new inertial Mann-type Tseng’s extragradient method to approximate the solution of this problem in real Hilbert spaces. Strong convergence of the proposed scheme to a minimum-norm solution of the problem is established when the associated single-valued operators are monotone and uniformly continuous with self-adaptive step size strategy. Moreover, we also study some classes of split inverse problems and provide some numerical implementations to illustrate our method and compare with a non-inertial version and a recently related method.
Original language | English |
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Pages (from-to) | 451-476 |
Number of pages | 26 |
Journal | Applied Set-Valued Analysis and Optimization |
Volume | 5 |
Issue number | 3 |
DOIs | |
Publication status | Published - 01 Jul 2023 |
Externally published | Yes |
Bibliographical note
Funding Information:This work was completed during the research visit of the second author to the Department of Mathematics, Clarkson University, Potsdam New York, United States. He is thankful to the Department of Mathematics at Clarkson University for hospitality. In particular, he is grateful to the fourth author for the invitation. The second author was supported by the National Research Foundation (NRF) of South Africa Incentive Funding for Rated Researchers (Grant Number 119903) and DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa (Grant Number 2022-087-OPA). The research of the third author was wholly supported by the University of KwaZulu-Natal, Durban, South Africa Postdoctoral Fellowship. He is grateful for the funding and financial support. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS and NRF.
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Keywords
- Inertial method
- Monotone inclusion problems
- Split inverse problems
- Tseng’s extragradient method
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Mathematics (miscellaneous)
- Modelling and Simulation
- Control and Optimization
- Applied Mathematics