1. Some global convergence properties of the Wei–Yao–Liu conjugate gradient method with inexact line search
- Author
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Zengxin Wei, Liliu Mo, and Sha Lu
- Subjects
Nonlinear conjugate gradient method ,Computational Mathematics ,Line search ,Applied Mathematics ,Conjugate gradient method ,Mathematical analysis ,Convergence (routing) ,Applied mathematics ,Conjugate residual method ,Derivation of the conjugate gradient method ,Gradient descent ,Gradient method ,Mathematics - Abstract
In [Z.Wei, S. Yao, L. Liu, The convergence properties of some new conjugate gradient methods, Applied Mathematics and Computation 183 (2006) 1341–1350], Wei et al. proposed a new conjugate gradient method called WYL method which has good numerical experiments and some excellent properties such as β k WYL ⩾ 0 . In this paper, we prove that while t k ⩽ 1 - c 2 L ‖ g k ‖ 2 ‖ d k ‖ 2 , the sufficient descent condition can be satisfied at each iteration of the WYL method. Based on this, the global convergence of the WYL method with the standard Armijo line search and the generalized Wolfe–Powell line search is established.
- Published
- 2011