A new three-term conjugate gradient algorithm based on the Dai-Liao and the Liu-Xu conjugate gradient methods

Yıl 2020, Cilt: 3 Sayı: 1, 35 - 46, 17.09.2020

Khalil K. Abbo

Öz

Based on the Dai-Laio and Liu-Xu methods, we develop a new three-term conjugate gradient method for solving large-scale unconstrained optimization problem,. The suggested method satisfies both the descent condition and the conjugacy condition. For uniformly convex function, under standard assumption the global convergence of the algorithm is proved. Finally, some numerical results of the proposed method are given.
Based on the Dai-Laio and Liu-Xu methods, we develop a new three-term conjugate gradient method for solving large-scale unconstrained optimization problem,. The suggested method satisfies both the descent condition and the conjugacy condition. For uniformly convex function, under standard assumption the global convergence of the algorithm is proved. Finally, some numerical results of the proposed method are given.
Based on the Dai-Laio and Liu-Xu methods, we develop a new three-term conjugate gradient method for solving large-scale unconstrained optimization problem,. The suggested method satisfies both the descent condition and the conjugacy condition. For uniformly convex function, under standard assumption the global convergence of the algorithm is proved. Finally, some numerical results of the proposed method are given.
Based on the Dai-Laio and Liu-Xu methods, we develop a new three-term conjugate gradient method for solving large-scale unconstrained optimization problem,. The suggested method satisfies both the descent condition and the conjugacy condition. For uniformly convex function, under standard assumption the global convergence of the algorithm is proved. Finally, some numerical results of the proposed method are given.
Based on the Dai-Laio and Liu-Xu methods, we develop a new three-term conjugate gradient method for solving large-scale unconstrained optimization problem,. The suggested method satisfies both the descent condition and the conjugacy condition. For uniformly convex function, under standard assumption the global convergence of the algorithm is proved. Finally, some numerical results of the proposed method are given.
Based on the Dai-Laio and Liu-Xu methods, we develop a new three-term conjugate gradient method for solving large-scale unconstrained optimization problem,. The suggested method satisfies both the descent condition and the conjugacy condition. For uniformly convex function, under standard assumption the global convergence of the algorithm is proved. Finally, some numerical results of the proposed method are given.
Based on the Dai-Laio and Liu-Xu methods, we develop a new three-term conjugate gradient method for solving large-scale unconstrained optimization problem,. The suggested method satisfies both the descent condition and the conjugacy condition. For uniformly convex function, under standard assumption the global convergence of the algorithm is proved. Finally, some numerical results of the proposed method are given.

Anahtar Kelimeler

descent methods, Conjugate gradient methods.

Kaynakça

• [1] N. Yilmaz and A. Sahiner, New global optimization method for non-smooth unconstrained continuous optimization. In: AIP Conference Proceedings. AIP Publishing LLC, 2017. p. 250002.‏
• [2] A. Sahiner and S. A. Ibrahem, A new global optimization technique by auxiliary function method in a directional search, Optim. Lett., 13(2) 2019, 309-323.‏
• [3] A. Sahiner, I. A. M. Abdulhamid and S. A. Ibrahem, A new filled function method with two parameters in a directional search, Journal of Multidisciplinary Modeling and Optimization, 2(1) 2019, 34-42.‏
• [4] A. Sahiner, S. A. Ibrahem and N. Yilmaz, Increasing the Effects of Auxiliary Function by Multiple Extrema in Global Optimization. In: Numerical Solutions of Realistic Nonlinear Phenomena. Springer, Cham, 2020, 125-143.
• [5] N. Andrei, An unconstrained optimization test function collection, Adv. Model. Optimization, (10) 2008, 147-161.
• [6] N. Andrei, Open Problems in Nonlinear Conjugate Gradient Algorithms for Unconstrained Optimization, Bulletin of the Malaysian Mathematical Sciences Society, (34) 2011, 319–330.
• [7] Y. Dai and C. Kou, A nonlinear conjugate gradient algorithm with an optimal property and an improved Wolfe line search, SIAM J. Optim., 23(1) 2013, 296-320.
• [8] Y. H. Dai and L.Z. Liao, New Conjugacy Conditions and Related Nonlinear Conjugate Gradient Methods, Applied Mathematics and Optimization, Springer-Verlag, New York, 2001.
• [9] E.D. Dolan and J.J. Mor´e, Benchmarking optimization software with performance profiles, Math. Programming, (91) 2002, 201-213.
• [10] R. Fletcher and C.M. Reeves, Function Minimization by Conjugate Gradients. Computer Journal, (7) 1964, 149-154.
• [11] M.R. Hestenes and E. Stiefel, Methods of Conjugate Gradients for Solving Linear Systems, Journal of Research of the National Bureau of Standards, 5 (49) 1952. [12] D. Liu and G. Xu, Symmetric Perry conjugate gradient method. Comput. Optim Appl., (56) 2013.
• [13] Y. Narushima, H. Yabe and J.A. Ford, A three-term conjugate gradient method with sufficient descent property for unconstrained optimization, SIAM Journal on Optimization, (21) 2013, 212-230.
• [14] A. Perry, (1978). A Modified Conjugate Gradient Algorithms. Operations Research, 26, PP. 1073–1078.
• [15] E. Polak and G. Ribiére, Note sur la convergence de directions conjuguée, Revue Francaise Information, (16) 1969, 35-43.
• [16] M. J. D. Powell, Nonconvex Minimization Calculations and the Conjugate Gradient Method. in : Numerical Analysis (Dundee,1983), In Lecture Notes in mathematics, Springer-Verlag, Berlin, 1066, 122-141, 1984.
• [17] D. F. Shanno, Conjugate gradient methods with inexact searches, Mathematics of Operations Research, (3) 1996, 244-256.
• [18] W. Sun and Y. Yuan, Optimization Theory and Methods, Nonlinear programming, Springer Science, Business Media, LLC., New York, 2006.
• [19] M. Wolfe, Numerical Methods For Unconstrained Optimization An Introduction, New York: Van Nostraned Reinhold, 1978.
• [20] G. Zoutendijk, Nonlinear Programming, Computational Methods. Integer and Nonlinear Programming (J. Abadie ED.), North-Holland, Amsterdam, 1970.