A descent generalized RMIL spectral gradient algorithm for optimization problems

• Autorzy: Sulaiman Ibrahim M. , Kaelo P. , Khalid Ruzelan , Nawawi Mohd Kamal M.

Identyfikatory

DOI

10.61822/amcs-2024-0016

• Języki publikacji: EN

Abstrakty

EN

This study develops a new conjugate gradient (CG) search direction that incorporates a well defined spectral parameter while the step size is required to satisfy the famous strong Wolfe line search (SWP) strategy. The proposed spectral direction is derived based on a recent method available in the literature, and satisfies the sufficient descent condition irrespective of the line search strategy and without imposing any restrictions or conditions. The global convergence results of the new formula are established using the assumption that the gradient of the defined smooth function is Lipschitz continuous. To illustrate the computational efficiency of the new direction, the study presents two sets of experiments on a number of benchmark functions. The first experiment is performed by setting uniform SWP parameter values for all the algorithms considered for comparison. For the second experiment, the study evaluates the performance of all the algorithms by considering the exact SWP parameter values used for the numerical experiments as reported in each work. The idea of these experiments is to study the influence of parameters in the computational efficiency of various CG algorithms. The results obtained demonstrate the effect of the parameter value on the robustness of the algorithms.

Słowa kluczowe

EN

optimization model; spectral CG algorithm; global convergence; line search strategy

PL

model optymalizacji; algorytm spektralny; zbieżność globalna

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2024
• Tom: Vol. 34, no. 2
• Strony: 225--233
• Opis fizyczny: Bibliogr. 30 poz., wykr.

Twórcy

autor

Sulaiman Ibrahim M.

• Institute of Strategic Industrial Decision Modelling, Northern University of Malaysia (UUM), Sintok, 06010, Kedah, Malaysia
• Faculty of Education and Arts, Sohar University, 3111 Al Jamiah Street, Sohar 311, Oman

autor

Kaelo P.

• Department of Mathematics, University of Botswana, 4775 Notwane Rd, Private Bag UB00704, Gaborone, Botswana

autor

Khalid Ruzelan

• Institute of Strategic Industrial Decision Modelling, Northern University of Malaysia (UUM), Sintok, 06010, Kedah, Malaysia

autor

Nawawi Mohd Kamal M.

• Institute of Strategic Industrial Decision Modelling, Northern University of Malaysia (UUM), Sintok, 06010, Kedah, Malaysia

Bibliografia

• [1] Amini, K. and Faramarzi, P. (2023). Global convergence of a modified spectral three-term CG algorithm for nonconvex unconstrained optimization problems, Journal of Computational and Applied Mathematics 417: 114630.
• [2] Andrei, N. (2007a). A scaled BFGS preconditioned conjugate gradient algorithm for unconstrained optimization, Applied Mathematics Letters 20(6): 645-650.
• [3] Andrei, N. (2007b). Scaled conjugate gradient algorithms for unconstrained optimization, Computational Optimization and Applications 38: 401-416.
• [4] Andrei, N. (2008). An unconstrained optimization test functions collection, Advanced Modeling and Optimization 10(1): 147-161.
• [5] Awwal, A., Sulaiman, M., Maulana, M., Kumam, P. and Sitthithakerngkiet, K. (2021). Spectral RMIL+ conjugate gradient method for unconstrained optimization with applications in portfolio selection and motion control, IEEE Access 9: 75398-75414.
• [6] Awwal, A., Wang, L., Kumam, P., Sulaiman, M., Salisu, S., Salihu, N. and Yodjai, P. (2023). Generalized RMIL conjugate gradient method under the strong Wolfe line search with application in image processing, Mathematical Methods in the Applied Sciences 2023: 1-13.
• [7] Babaie-Kafaki, S. and Ghanbari, R. (2017). An optimal extension of the Polak-Ribiere-Polyak conjugate gradient method, Numerical Functional Analysis and Optimization 38(9): 1115-1124.
• [8] Birgin, E. and Martinez, J. (2001). A spectral conjugate gradient method for unconstrained optimization, Applied Mathematics and Optimization 43: 117-128.
• [9] Collignon, T.P. and van Gijzen, M.B. (2010). Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids, International Journal of Applied Mathematics and Computer Science 20(1): 109-121, DOI: 10.2478/v10006-010-0008-4.
• [10] Dai, Y., Han, J., Liu, G., Sun, D., Yin, H. and Yuan, Y. (2000). Convergence properties of nonlinear conjugate gradient methods, SIAM Journal on Optimization 10(2): 345-358.
• [11] Dai, Z. (2016). Comments on a new class of nonlinear conjugate gradient coefficients with global convergence properties, Applied Mathematics and Computation 276: 297-300.
• [12] Dolan, E.D. and Moré, J.J. (2002). Benchmarking optimization software with performance profiles, Mathematical Programming 91(2): 201-213.
• [13] Hager, W. and Zhang, H. (2006). A survey of nonlinear conjugate gradient methods, Pacific Journal of Optimization 2(1): 35-58.
• [14] Hestenes, M. and Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems, Journal of Research of the National Institute of Standards and Technology 49(6): 409-435.
• [15] Hu, Q., Zhang, H. and Chen, Y. (2022). Global convergence of a descent PRP type conjugate gradient method for nonconvex optimization, Applied Numerical Mathematics 173: 38-50.
• [16] Koko, J. (2004). Newton’s iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition, International Journal of Applied Mathematics and Computer Science 14(1): 13-18.
• [17] Liu, J., Feng, Y. and Zou, L. (2018). Some three-term conjugate gradient methods with the inexact line search condition, Calcolo 55(16): 16.
• [18] Novkaniza, F., Malik, M., Sulaiman, I. and Aldila, D. (2022). Modified spectral conjugate gradient iterative scheme for unconstrained optimization problems with application on COVID-19 model, Frontiers in Applied Mathematics and Statistics 8: 1014956.
• [19] Perry, A. (1978). A modified conjugate gradient algorithm, Operations Research 26(6): 1073-1078.
• [20] Polak, B. and Ribiere, G. (1969). Note sur la convergence de methodes de directions conjugues, Mathematical Modelling and Numerical Analysis 16(3): 35-43.
• [21] Polyak, B.T. (1969). The conjugate gradient method in extreme problems, USSR Computational Mathematics and Mathematical Physics 9(4): 94-112.
• [22] Rivaie, M., Mamat, M., June, L. and Mohd, I. (2012). A new class of nonlinear conjugate gradient coefficients with global convergence properties, Applied Mathematics and Computation 218(22): 11323-11332.
• [23] Sabiu, J., Ibrahim, I.S., Kaelo, P., Malik, M. and Saadi, A.K. (2024). An optimal choice Dai-Liao conjugate gradient algorithm for unconstrained optimization and portfolio selection, AIMS Mathematics 9(1): 642-664.
• [24] Salihu, N., Kumam, P., Awwal, A., Sulaiman, I. and Seangwattana, T. (2023). The global convergence of spectral RMIL conjugate gradient method for unconstrained optimization with applications to robotic model and image recovery, PLoS ONE 18(3): e0281250.
• [25] Sulaiman, I., Malik, M., Awwal, A., Kumam, P., Mamat, M. and Al-Ahmad, S. (2022). On three-term conjugate gradient method for optimization problems with applications on Covid-19 model and robotic motion control, Advances in Continuous and Discrete Models 2022(1): 1-22.
• [26] Sulaiman, I., Sukono, S., Supian, S. and Mamat, M. (2019). New class of hybrid conjugate gradient coefficients with guaranteed descent and efficient line search, 7th International Conference on Global Optimization and Its Application (ICoGOIA 2018), Bali, Indonesia, p. 012021.
• [27] Wan, Z., Yang, Z. and Wang, Y. (2011). New spectral PRP conjugate gradient method for unconstrained optimization, Applied Mathematics Letters 24(1): 16-22.
• [28] Xia, Z., Wang, X., Sun, X. and Wang, Q. (2015). A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data, IEEE Transactions on Parallel and Distributed Systems 27(2): 340-352.
• [29] Zhang, L., Zhou, W. and Li, D.-H. (2006). A descent modified Polak Ribiere Polyak conjugate gradient method and its global convergence, IMA Journal of Numerical Analysis 26(4): 629-640.
• [30] Zoutendijk, G. (1970). Nonlinear programming computational methods, in J. Abadie (Ed.), Integer and Nonlinear Programming, North-Holland, Amsterdam, pp. 37-86.