Two efficient modifications of AZPRP conjugate gradient method with sufficient descent property

The conjugate gradient method can be applied in many fields, such as neural networks, image restoration, machine learning, deep learning, and many others. Polak–Ribiere–Polyak and Hestenses–Stiefel conjugate gradient methods are considered as the most efficient methods to solve nonlinear optimizatio...

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Bibliographic Details
Published in:Journal of inequalities and applications 2022-01, Vol.2022 (1), p.1-21, Article 14
Main Authors: Salleh, Zabidin, Almarashi, Adel, Alhawarat, Ahmad
Format: Article
Language:English
Subjects:
Analysis
Applications of Mathematics
Conjugate gradient method
Convergence
Deep learning
Global convergence
Image restoration
Machine learning
Mathematics
Mathematics and Statistics
Methods
Neural networks
Optimization
Polak–Ribiere–Polyak method
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Summary:The conjugate gradient method can be applied in many fields, such as neural networks, image restoration, machine learning, deep learning, and many others. Polak–Ribiere–Polyak and Hestenses–Stiefel conjugate gradient methods are considered as the most efficient methods to solve nonlinear optimization problems. However, both methods cannot satisfy the descent property or global convergence property for general nonlinear functions. In this paper, we present two new modifications of the PRP method with restart conditions. The proposed conjugate gradient methods satisfy the global convergence property and descent property for general nonlinear functions. The numerical results show that the new modifications are more efficient than recent CG methods in terms of number of iterations, number of function evaluations, number of gradient evaluations, and CPU time.
ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-021-02746-0