A conjugate gradient projection method with restart procedure for solving constraint equations and image restorations

The conjugate gradient projection method is one of the most effective methods for solving large-scale nonlinear monotone convex constrained equations. In this paper, a new search direction with restart procedure is proposed, and a self-adjusting line search criterion is improved, then a three-term c...

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Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 70; no. 3; pp. 2255 - 2284
Main Authors: Jiang, Xianzhen, Huang, Zefeng, Yang, Huihui
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2024
Springer Nature B.V
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Constraints
Design
Lipschitz condition
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Methods
Optimization
Original Research
Theory of Computation
Global convergence
Nonlinear constrained equations
Three-term conjugate gradient projection method
Restart procedure
Image restorations
ISSN:1598-5865, 1865-2085
Online Access:Get full text
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Summary:The conjugate gradient projection method is one of the most effective methods for solving large-scale nonlinear monotone convex constrained equations. In this paper, a new search direction with restart procedure is proposed, and a self-adjusting line search criterion is improved, then a three-term conjugate gradient projection method is designed to solve the large-scale nonlinear monotone convex constrained equations and image restorations. Without using the Lipschitz continuity of these equations, the presented method is proved to be globally convergent. Moreover, its R-linear convergence rate is attained under Lipschitz continuity and the usual assumptions. Finally, large-scale numerical experiments for the convex constraint equations and image restorations have been performed, which show that the new method is effective.
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-024-02044-0