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A new class of efficient and globally convergent conjugate gradient methods in the Dai-Liao family. (English) Zbl 1328.90143

Summary: In this paper, we propose a new conjugate gradient (CG) method which belongs to the CG methods of Y. H. Dai and L. Z. Liao family [Appl. Math. Optim. 43, No. 1, 87–101 (2001; Zbl 0973.65050)]. S. Babaie-Kafaki et al. [J. Comput. Appl. Math. 234, No. 5, 1374–1386 (2010; Zbl 1202.65071)] made some modifications on the H. Yabe and M. Takano’s CG approach [Comput. Optim. Appl. 28, No. 2, 203–225 (2004; Zbl 1056.90130)] and received some appealing results in theory and practice. Here, we introduce an efficient updating rule for the parameters of the Yabe and Takano’s CG algorithm. Under some standard assumptions, we establish the global convergence property of the new suggested algorithm on uniformly convex and general functions. Numerical results on some testing problems from CUTEr collection show the priority of the proposed method to some existing CG methods in practice.

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
49M37 Numerical methods based on nonlinear programming

Software:

CUTEr
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References:

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