A new optimization method based on Perry's idea through the use of the matrix power

• Autorzy: Hafaidia Imane , Benrabia Noureddine , Ghiat Mourad , Guebbai Hamza

Identyfikatory

DOI

10.17512/jamcm.2021.4.03

• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to present a new conjugate gradient method for solving unconstrained nonlinear optimization problems, based on Perry’s idea. An accelerated adaptive algorithm is proposed, where our search direction satisfies the sufficient descent condition. The global convergence is analyzed using the spectral analysis. The numerical results are described for a set of standard test problems, and it is shown that the performance of the proposed method is better than that of the CG-DESCENT, the mBFGS and the SPDOC.

Słowa kluczowe

EN

conjugate gradient method; symmetrical technique; spectral analysis; global convergence; unconstrained optimization

PL

metoda gradientu sprzężonego; technika symetryczna; analiza spektralna; globalna konwergencja

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2021
• Tom: Vol. 20, nr 4
• Strony: 29--41
• Opis fizyczny: Bibliogr. 27 poz., rys.

Twórcy

autor

Hafaidia Imane

• Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma B.P. 401 Guelma 24000 Algiérie

autor

Benrabia Noureddine

• Département de Mathématiques, Université Mohamed-Chérif Messaadia Souk Ahras B.P. 1553, 41000, Souk Ahras, Algeria

autor

Ghiat Mourad

• Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma B.P. 401 Guelma 24000 Algiérie

autor

Guebbai Hamza

• Laboratoire de Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945 Guelma B.P. 401 Guelma 24000 Algiérie

Bibliografia

• [1] Baluch, B., Salleh, Z., & Alhawarat, A. (2018). A new modified three-term Hestenes-Stiefel conjugate gradient method with sufficient descent property and its global convergence. Journal of Optimization, 6, 1-13.
• [2] Sabi’u, J., Muangchoo, K., Shah, A., Abubakar, A.B., & Aremu, K.O. (2021). An inexact optimal hybrid conjugate gradient method for solving symmetric nonlinear equations. Symmetry, 13(10), 1829.
• [3] Salleh, Z., Alhamzi, G., Masmali, I., & Alhawarat, A. (2021). A modified Liu and Storey conjugate gradient method for large scale unconstrained optimization problems. Algorithms, 14(8), 227.
• [4] Sabi’u, J., Shah, A., & Waziri, M.Y. (2020). Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations. Applied Numerical Mathematics, 153, 217-233.
• [5] Waziri, M.Y., Ahmed, K., & Sabi’u, J. (2019). A family of Hager-Zhang conjugate gradient methods for system of monotone nonlinear equations. Applied Mathematics and Computation, 361, 645-660.
• [6] Sabi’u, J., Shah, A., & Waziri, M.Y. (2021). A modified Hager-Zhang conjugate gradient method with optimal choices for solving monotone nonlinear equations. International Journal of Computer Mathematics, 1-23.
• [7] Hestenes, M.R., & Stiefel, E. (1952). Methods of Conjugate Gradients for Solving Linear Systems. (Vol. 49, No. 1), Washington, DC: NBS.
• [8] Fletcher, R., & Powell, M.J. (1963). A rapidly convergent descent method for minimization. The Computer Journal, 6(2), 163-168.
• [9] Polak, E., & Ribiere, G. (1969). Note sur la convergence de méthodes de directions conjuguées. ESAIM: Mathematical Modelling and Numerical Analysis-Modélisation Mathématique et Analyse Numérique, 3(R1), 35-43.
• [10] Cardenas, S. (1991). Efficient generalized conjugate gradient algorithms. I. Theory. Journal of Optimization Theory and Applications, 69(1), 129-137.
• [11] Hager, W.W., & Zhang, H. (2005). A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM Journal on Optimization, 16(1), 170-192.
• [12] Abubakar, A.B., Sabi’u, J., Kumam, P., & Shah, A. (2021). Solving nonlinear monotone operator equations via modified sr1 update. Journal of Applied Mathematics and Computing, 1-31.
• [13] Zhou, W. (2020). A modified BFGS type quasi-Newton method with line search for symmetric nonlinear equations problems. Journal of Computational and Applied Mathematics, 367, 112454.
• [14] Perry, A. (1978). A modified conjugate gradient algorithm. Operations Research, 26(6), 1073-1078.
• [15] Livieris, I.E., & Pintelas, P. (2015). A modified Perry conjugate gradient method and its global convergence. Optimization Letters, 9(5), 999-1015.
• [16] Andrei, N. (2017). Accelerated adaptive Perry conjugate gradient algorithms based on the self-scaling memoryless BFGS update. Journal of Computational and Applied Mathematics, 325, 149-164.
• [17] Waziri, M.Y., Hungu, K.A., & Sabi’u, J. (2020). Descent Perry conjugate gradient methods for systems of monotone nonlinear equations. Numerical Algorithms, 85(3), 763-785.
• [18] Andrei, N.(2007). Scaled conjugate gradient algorithms for unconstrained optimization. Computational Optimization and Applications, 38, 3, 401-416.
• [19] Yao, S., He, D., & Shi, L. (2018). An improved Perry conjugate gradient method with adaptive parameter choice. Numerical Algorithms, 78(4), 1255-1269.
• [20] Dongyi, L., & Genqi, X. (2011). Applying Powell’s symmetrical technique to conjugate gradient methods. Computational Optimization and Applications, 49(2), 319-334.
• [21] Andrei, N. (2010). Another accelerated conjugate gradient algorithm with guaranteed descent and conjugacy conditions for large-scale unconstrained optimization. No. 7. ICI Technical Report.
• [22] Hager, W.W., & Zhang, H. (2006). Algorithm 851: CG-DESCENT, a conjugate gradient method with guaranteed descent. ACM Transactions on Mathematical Software (TOMS), 32(1), 113-137.
• [23] Shanno, D.F. (1978). Conjugate gradient methods with inexact searches. Mathematics of Operations Research, 3(3), 244-256.
• [24] Liu, D., & Xu, G. (2013). Symmetric Perry conjugate gradient method. Computational Optimization and Applications, 56(2), 317-341.
• [25] Andrei, N. (2008). An unconstrained optimization test functions collection. Advanced Modeling and Optimization, 10, 1, 147-161.
• [26] Dolan, E.D., & Mor ́e, J.J. (2002). Benchmarking optimization software with performance profiles. Mathematical Programming, 91(2), 201-213.
• [27] Zoutendijk, G.(1970). Nonlinear programming, computational methods. Integer and Nonlinear Programming, 37-86.