A New Modified Conjugate Gradient for Nonlinear Minimization Problems
DOI:
https://doi.org/10.25271/sjuoz.2022.10.4.933Keywords:
Unconstrained Nonlinear minimization, Method of Conjugate Gradient, Descent property, property of the Sufficient Descent and property of the Global convergenceAbstract
The conjugate gradient is a highly effective technique to solve the unconstrained nonlinear minimization problems and it is one of the most well-known methods. It has a lot of applications. For large-scale, unconstrained minimization problems, conjugate gradient techniques are widely applied. In this paper, we will suggest a new parameter of conjugate gradient to solve the nonlinear unconstrained minimization problems, based on parameter of Dai and Liao. We will study the property of the descent ,the property of the sufficient descent and property of the global convergence a new method. We introduce some numerical data to prove the efficacy of the our method.
References
Dai, Y.H. , Han, J., Liu, G., Sun, D., Yin, H. & Yuan, Y. X. (2000). Convergence properties of nonlinear conjugate gradient methods. SIAM J. Optim., 10(2), 345–358.
Dai, Y.H. & Liao, l. z. (2001). New conjugacy conditions and related nonlinear conjugate gradient methods. Appl. Math. Optim, 43, 87–101.
Dai, Y.H. & Yuan, Y. (1999). A nonlinear conjugate gradient with a strong global convergence properties. SIAM J. Optim., 10(1), 177–182.
Dai , Y. H. & Yuan, Y. (1996). Convergence properties of the Fletcher-Reeves method. IMA J. Numer. Anal., 16(2), 155–164.
Deng, N.Y. & Li, Z. (1995). Global convergence of three terms conjugate gradient methods. Method and Sofeware, 4, 273–282.
Fletcher, R., and Reeves, C. (1964). Function minimization by conjugate gradients. Comput. J., 7, 149–154.
Gilbert J. C. & Nocedal, J. (1992). Global convergence properties of conjugate gradient methods for optimization. SIAM. J. Optim., 2(1), 21–42.
Grippo, L. & Lucidi, S. (1997). A global convergent version of the Polak-Ribiere conjugate gradient method. Math. Prog., 78, 375–391.
Hager, W, & Zhang, H. C. (2005). A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim, 16, 170–192.
Hestenes, M.R. & Stiefel, E. (1952). Method of conjugate gradient for solving linear equations. J.Res. Nat. Bur. Stand, 49, 409–436.
Hu, Y.F. & Storey, C. (1991). Global convergence result for conjugate gradient methods. J. Optim. Theory Appl., 71, 399–405.
Liu, Y. & Storey, C. (1991). Efficient generalized conjugate gradient algorithms, Part 1: Theory. JOTA, 69, 129–137.
Polak, E. & Ribiere, G. (1969). Note sur la convergence de directions conjugees. Rev. Francaise Inform. Recherche Operationelle 3, 16, 35–43.
Powell, M. J. D. (1977). Restart procedures of the conjugate gradient method. Math. Prog., 2, 241–254.
Zhang, L. , Zhou, W. & Li, D. (2006). Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search. Numer. Math., 104, 561–572.
Zhang L., Zhou W.J., L. D. H. (2006). A descent modified Polak-Ribiere-Polyak conjugate gradient method and its global convergence. IMA Journal of Numerical Analysis, 26, 629–640.
Zoutendijk, G. (1970). Nonlinear programming, computational methods, in Integer and Nonlinear Programming. J. Abadie, North-Holl, 37–86.
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