New conjugacy conditions and related nonlinear conjugate gradient methods. (English) Zbl 0973.65050

Dai, Y.-H.; Liao, L.-Z.

Appl. Math. Optim. 43, No. 1, 87-101 (2001).

Authors’ abstract: Conjugate gradient methods are a class of important methods for unstrained optimization, especially when the dimension is large. This paper proposes a new conjugacy condition, which considers an inexact line search scheme but reduces to the old one if the line search is exact. Based on the new conjugacy condition, two nonlinear conjugate gradient methods are constructed. Convergence analysis for the two methods is provided. Our numerical results show that one of the methods is very efficient for the given test problems.

Reviewer: Klaus Schittkowski (Bayreuth)

MSC:

65K05	Numerical mathematical programming methods
90C30	Nonlinear programming
90C53	Methods of quasi-Newton type

Keywords:

numerical examples; convergence; unstrained optimization; conjugacy condition; inexact line search; nonlinear conjugate gradient methods

Software:

minpack