Solving constrained nonlinear equations with an inertial-based hybrid three-term CGP algorithm: application to image denoising

In this paper, an inertial-based hybrid three-term conjugate gradient projection (CGP) algorithm is proposed for solving constrained nonlinear equations. This algorithm exhibits several key theoretical features: (1) A hybrid three-term search direction is constructed using the hybrid technique, ensu...

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Bibliographic Details
Published in:Journal of applied mathematics & computing Vol. 71; no. Suppl 1; pp. 1109 - 1136
Main Authors: Li, Dandan, Li, Yong, Wang, Songhua
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2025
Springer Nature B.V
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Constraints
Iterative methods
Lipschitz condition
Mathematical and Computational Engineering
Mathematics
Mathematics and Statistics
Mathematics of Computing
Noise reduction
Nonlinear equations
Original Research
Theory of Computation
Nonlinear equations
Inertial acceleration technique
65K05
90C56
Conjugate gradient projection method
Convergence analysis
Image denoising
ISSN:1598-5865, 1865-2085
Online Access:Get full text
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Summary:In this paper, an inertial-based hybrid three-term conjugate gradient projection (CGP) algorithm is proposed for solving constrained nonlinear equations. This algorithm exhibits several key theoretical features: (1) A hybrid three-term search direction is constructed using the hybrid technique, ensuring both sufficient descent and trust region properties. (2) An inertial extrapolation step is incorporated into the algorithm, enhancing its efficiency. (3) The global convergence of the algorithm is rigorously analyzed, without relying on the Lipschitz continuity of the nonlinear equations. (4) Preliminary numerical experiments on standard constrained nonlinear equations and image denoising problems are reported, which demonstrate the effectiveness and superiority of the proposed algorithm when compared to existing methods.
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ISSN:1598-5865
1865-2085
DOI:10.1007/s12190-025-02525-w