Zhang, Li; Zhou, Weijun; Li, Donghui Global convergence of a modified Fletcher-Reeves conjugate gradient method with Armijo-type line search. (English) Zbl 1103.65074 Numer. Math. 104, No. 4, 561-572 (2006). Summary: In this paper, we are concerned with the conjugate gradient methods for solving unconstrained optimization problems. It is well-known that the direction generated by a conjugate gradient method may not be a descent direction of the objective function. In this paper, we take a little modification to the Fletcher-Reeves (FR) method such that the direction generated by the modified method provides a descent direction for the objective function. This property depends neither on the line search used, nor on the convexity of the objective function. Moreover, the modified method reduces to the standard FR method if line search is exact. Under mild conditions, we prove that the modified method with Armijo-type line search is globally convergent even if the objective function is nonconvex. We also present some numerical results to show the efficiency of the proposed method. Cited in 5 ReviewsCited in 131 Documents MSC: 65K05 Numerical mathematical programming methods 90C30 Nonlinear programming Keywords:convergence; conjugate gradient methods; unconstrained optimization; Fletcher-Reeves method; Armijo-type line search; numerical results Software:CUTE; L-BFGS; SCALCG; minpack; CUTEr × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Al-Baali M. (1985) Descent property and global convergence of the Fletcher–Reeves method with inexact line search. IMA J. Numer. Anal. 5, 121–124 · Zbl 0578.65063 · doi:10.1093/imanum/5.1.121 [2] Andrei, N.: Scaled conjugate gradient algorithms for unconstrained optimization. Comput. Optim. Appl. (to apper) · Zbl 1168.90608 [3] Birgin E., Martínez J.M. 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