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Wei, Zengxin; Yao, Shengwei; Liu, Liying

The convergence properties of some new conjugate gradient methods. (English) Zbl 1116.65073

Appl. Math. Comput. 183, No. 2, 1341-1350 (2006).
A new conjugate gradient formula \(\beta^*_k\) is given to compute the search directions for unconstrained optimization problems. General convergence results for the proposed formula with exact Wolfe-Powell line search and Grippo-Lucidi line search. Under these line searches and some assumptions, the global convergence properties of the given methods are discussed. The given formula \(\beta^*_k\geq 0\) has the similar form as \(\beta^{PRP}_k\). Some numerical results show that the proposed methods are efficient.
Reviewer: Stefan Mititelu (Bucureşti)

Cited in 9 Reviews
Cited in 69 Documents

MSC:

65K05 Numerical mathematical programming methods
90C59 Approximation methods and heuristics in mathematical programming
90C30 Nonlinear programming

Keywords:

nonlinear optimization; conjugate gradient; exact line search; inexact line search; global convergence; unconstrained optimization problem; numerical results
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\textit{Z. Wei} et al., Appl. Math. Comput. 183, No. 2, 1341--1350 (2006; Zbl 1116.65073)
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