The proof of the sufficient descent condition of the Wei-Yao-Liu conjugate gradient method under the strong Wolfe-Powell line search. (English) Zbl 1131.65049

This short article investigates the sufficient descent condition of a new conjugate gradient method. In the first section an overview of conjugate gradient methods is presented and, in particular, the new approach by Z. Wei, S. Yao and L. Liu [ibid. 183, No. 2, 1341–1350 (2006; Zbl 1116.65073)]. In the second section the main result of this article is presented, namely, that for the case of the parameter \(\sigma<1/4\) the Wei-Yai-Liu conjugate gradient method possesses the sufficient decent condition.


65K05 Numerical mathematical programming methods
90C52 Methods of reduced gradient type
90C30 Nonlinear programming


Zbl 1116.65073
Full Text: DOI


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