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Global convergence of a class of unconstrained optimal methods that include the conjugate descent method. (Chinese. English summary) Zbl 1015.90078

Summary: The conjugate descent method introduced by Fletcher (1987) is one of the conjugate gradient methods. The authors present a class of unconstrained optimal methods which include the conjugate-descent method. Using the inexact line-search model put forward by Y. Dai and Y. Yuan [Adv. Math. Beijing 25, 552-562 (1996; Zbl 0871.49028)], we give search conditions that can ensure the descent property and global convergence. The convergence condition is related to the conjugate descent method is consistent with that given by Y. Dai and Y. Yuan [IMA J. Numer. Anal. 16, 155-164 (1996; Zbl 0851.68049)].

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
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