Double Inertial Proximal Gradient Algorithms for Convex Optimization Problems and Applications

In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide...

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Bibliographic Details
Published in:Acta mathematica scientia Vol. 43; no. 3; pp. 1462 - 1476
Main Authors: Kankam, Kunrada, Cholamjiak, Prasit
Format: Journal Article
Language:English
Published: Singapore Springer Nature Singapore 01.05.2023
Springer Nature B.V
School of Science,University of Phayao,Phayao 56000,Thailand
Edition:English Ed.
Subjects:
Algorithms
Analysis
Convex analysis
Mathematics
Mathematics and Statistics
Optimization
65K05
90C30
forward-backward algorithm
convex minimization
90C25
inertial technique
weak convergence
ISSN:0252-9602, 1572-9087
Online Access:Get full text
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Summary:In this paper, we propose double inertial forward-backward algorithms for solving unconstrained minimization problems and projected double inertial forward-backward algorithms for solving constrained minimization problems. We then prove convergence theorems under mild conditions. Finally, we provide numerical experiments on image restoration problem and image inpainting problem. The numerical results show that the proposed algorithms have more efficient than known algorithms introduced in the literature.
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ISSN:0252-9602
1572-9087
DOI:10.1007/s10473-023-0326-x