×
Lotfi, M.; Hosseini, S. Mohammad

An efficient hybrid conjugate gradient method with sufficient descent property for unconstrained optimization. (English) Zbl 1511.65049

Optim. Methods Softw. 37, No. 5, 1725-1739 (2022).
Summary: In order to take advantage of the strong theoretical properties of the FR method and computational efficiency of the \(PRP+\) method, we present a new hybrid conjugate gradient method based on the convex combination of these methods. In our method, the search directions satisfy the sufficient descent condition independent of any line search. Under some standard assumptions, we established global convergence property of our proposed method for general functions. Numerical comparisons on some test problems from the CUTEst library illustrate the efficiency and robustness of our proposed method in practice.

Cited in 1 Document

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming

Keywords:

conjugate gradient method; sufficient descent; unconstrained optimization; global convergence

Software:

CUTEst
Cite Review PDF
Full Text: DOI

References:

[1] Aminifard, Z.; Babaie-Kafaki, S., A modified descent Polak-Ribière-Polyak conjugate gradient method with global convergence property for nonconvex functions, 56, 1-11 · Zbl 1415.90147
[2] Andrei, N., Numerical comparison of conjugate gradient algorithms for unconstrained optimization, Stud. Inform. Control., 16, 333-352 (2007)
[3] Andrei, N., Another hybrid conjugate gradient algorithm for unconstrained optimization, Numer. Algor., 47, 143-156 (2008) · Zbl 1141.65041
[4] Andrei, N., Hybrid conjugate gradient algorithm for unconstrained optimization, J. Optim. Theory Appl., 141, 249-264 (2009) · Zbl 1168.90017
[5] Andrei, N., Accelerated hybrid conjugate gradient algorithm with modified secant condition for unconstrained optimization, Numer. Algor., 54, 1, 23-46 (2010) · Zbl 1192.65074
[6] Andrei, N., Nonlinear Conjugate Gradient Methods for Unconstrained Optimization, Springer Optimization and Its Applications, Vol. 158, 2020. · Zbl 1514.90250
[7] Babaie-Kafaki, S., A quadratic hybridization of Polak-Ribière-Polyak and Fletcher-Reeves conjugate gradient methods, J. Optim. Theory Appl., 154, 3, 916-932 (2012) · Zbl 1256.90050
[8] Babaie-Kafaki, S.; Fatemi, M.; Mahdavi-Amiri, N., Two effective hybrid conjugate gradient algorithms based on modified BFGS updates, Numer. Algor., 58, 315-331 (2011) · Zbl 1277.90149
[9] Babaie-Kafaki, S.; Ghanbari, R., A hybridization of the Polak-Ribière-Polyak and Fletcher-Reeves conjugate gradient methods, Numer. Algor., 68, 3, 481-495 (2015) · Zbl 1311.65066
[10] Birgin, E. G.; Martínez, J. M., A spectral conjugate gradient method for unconstrained optimization, Appl. Math. Optim., 43, 117-128 (2001) · Zbl 0990.90134
[11] Dai, Y. H.; Yuan, Y., A nonlinear conjugate gradient method with a strong global convergence property, SIAM J. Optim., 10, 177-182 (1999) · Zbl 0957.65061
[12] Dolan, E.; Moré, J., Benchmarking optimization software with performance profiles, Math., 91, 201-213 (2002) · Zbl 1049.90004
[13] Fletcher, R., Practical Methods of Optimization (1987), Wiley & Sons: Wiley & Sons, New York · Zbl 0905.65002
[14] Fletcher, R.; Reeves, C. M., Function minimization by conjugate gradients, Comput. J., 7, 2, 149-154 (1964) · Zbl 0132.11701
[15] Gould, N. I.M.; Orban, D.; Toint, P. L., CUTEst : A constrained and unconstrained testing environment with safe threads for mathematical optimization, Comput. Optim. Appl., 60, 3, 545-557 (2015) · Zbl 1325.90004
[16] Hager, W. W.; Zhang, H. A., New conjugate gradient method with guaranteed descent and an efficient line search, SIAM J. Optim., 16, 170-192 (2005) · Zbl 1093.90085
[17] Hestenes, M. R.; Stiefel, E. L., Methods of conjugate gradients for solving linear systems, J. Res. Natl. Bur. Stand., 409-436 (1952) · Zbl 0048.09901
[18] Jiang, X.; Jian, J., Improved Fletcher-Reeves and Dai-Yuan conjugate gradient methods with the strong Wolfe line search, J. Comput. Appl. Math., 348, 525-534 (2019) · Zbl 1409.90092
[19] Kou, C. X.; Dai, Y. H., A modified self-scaling memoryless Broyden-Fletcher-Goldfarb-Shanno method for unconstrained optimization, J. Optim. Theory. Appl., 165, 1, 209-224 (2015) · Zbl 1319.49042
[20] Li, M., A family of three-term nonlinear conjugate gradient methods close to the memoryless BFGS method, Optim. Lett., 12, 8, 1911-1927 (2018) · Zbl 1412.90165
[21] Liu, Y.; Storey, C., Efficient generalized conjugate gradient algorithms, I. Theory. J. Optim. Theory Appl., 69, 1, 129-137 (1991) · Zbl 0702.90077
[22] Livieris, I. E.; Tampakas, V.; Pintelas, P., A descent hybrid conjugate gradient method based on the memoryless BFGS update, Numer. Algor., 79, 4, 1169-1185 (2018) · Zbl 06986853
[23] Narushima, Y.; Yabe, H.; Ford, J. A., A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM J. Optim., 21, 212-230 (2011) · Zbl 1250.90087
[24] Nocedal, J.; Wright, S. J., Numerical Optimization (2006), Springer: Springer, New York · Zbl 1104.65059
[25] Polak, E.; Ribière, G., Note sur la convergence des mthodes de directions conjuguées, Rev. Fr. Inform. Rech. Oper., 16, 35-43 (1952) · Zbl 0174.48001
[26] Polyak, E. T., The conjugate gradient method in extreme problems, USSR Comp. Math. Math. Phys., 9, 94-112 (1969) · Zbl 0229.49023
[27] Touati-Ahmed, D.; Storey, C., Efficient hybrid conjugate gradient techniques, J. Optim. Theory Appl., 64, 2, 379-397 (1990) · Zbl 0666.90063
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.