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01-09-2014 | Research paper

On the sufficient descent condition of the Hager-Zhang conjugate gradient methods

Author: Saman Babaie-Kafaki

Published in: 4OR | Issue 3/2014

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Abstract

Based on an eigenvalue study, the sufficient descent condition of an extended class of the Hager-Zhang nonlinear conjugate gradient methods is established. As an interesting result, it is shown that the search directions of the CG_Descent algorithm satisfy the sufficient descent condition \(d_k^Tg_k<-\frac{7}{8}||g_k||^2\).

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Babaie-Kafaki S (2012) A note on the global convergence theorem of the scaled conjugate gradient algorithms proposed by Andrei. Comput Optim Appl 52(2):409–414CrossRef

Dai YH, Han JY, Liu GH, Sun DF, Yin HX, Yuan YX (1999) Convergence properties of nonlinear conjugate gradient methods. SIAM J Optim 10(2):348–358

Dai YH (2001) New properties of a nonlinear conjugate gradient method. Numer Math 89(1):83–98CrossRef

Dai YH, Liao LZ (2001) New conjugacy conditions and related nonlinear conjugate gradient methods. Appl Math Optim 43(1):87–101CrossRef

Dai YH, Kou CX (2013) A nonlinear conjugate gradient algorithm with an optimal property and an improved Wolfe line search. SIAM J Optim 23(1):296–320CrossRef

Gilbert JC, Nocedal J (1992) Global convergence properties of conjugate gradient methods for optimization. SIAM J Optim 2(1):21–42CrossRef

Hager WW, Zhang H (2005) A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J Optim 16(1):170–192CrossRef

Hager WW, Zhang H (2006) Algorithm 851: CG_Descent, a conjugate gradient method with guaranteed descent. ACM Trans Math Softw 32(1):113–137CrossRef

Hager WW, Zhang H (2006) A survey of nonlinear conjugate gradient methods. Pac J Optim 2(1):35–58

Hestenes MR, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. J Res Nat Bur Stand 49(6):409–436CrossRef

Liu DC, Nocedal J (1989) On the limited memory BFGS method for large-scale optimization. Math Prog 45(3, Ser. B):503–528CrossRef

Nocedal J (1980) Updating quasi-Newton matrices with limited storage. Math Comput 35(151):773–782CrossRef

Polak E, Ribière G (1969) Note sur la convergence de méthodes de directions conjuguées. Rev Française Informat. Recherche Opérationnelle 3(16):35–43

Polyak BT (1969) The conjugate gradient method in extreme problems. USSR Comp. Math. Math. Phys. 9(4):94–112CrossRef

Powell MJD (1984) Nonconvex minimization calculations and the conjugate gradient method. In: Griffiths DF (ed) Numerical Analysis (Dundee, 1983), volume 1066 of Lecture Notes in Math. Springer, Berlin, pp 122–141

Sun W, Yuan YX (2006) Optimization theory and methods: nonlinear programming. Springer, New York

Title: On the sufficient descent condition of the Hager-Zhang conjugate gradient methods
Author: Saman Babaie-Kafaki
Publication date: 01-09-2014
Publisher: Springer Berlin Heidelberg
Published in: 4OR / Issue 3/2014
Print ISSN: 1619-4500
Electronic ISSN: 1614-2411
DOI: https://doi.org/10.1007/s10288-014-0255-6

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