Abstract
AbstractThe 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.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference24 articles.
1. Wolfe, P.: Convergence conditions for ascent methods. SIAM Rev. 11(2), 226–235 (1969)
2. Wolfe, P.: Convergence conditions for ascent methods. II: some corrections. SIAM Rev. 13(2), 185–188 (1971)
3. Hestenes, M.R., Stiefel, E.: Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stand. 49(6), 409–436 (1952)
4. Polak, E., Ribiere, G.: Note sur la convergence de méthodes de directions conjuguées. ESAIM: Math. Model. Numer. Anal. 3(R1), 35–43 (1969)
5. Liu, Y., Storey, C.: Efficient generalised conjugate gradient algorithms, part 1: theory. J. Optim. Theory Appl. 69(1), 129–137 (1991)
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