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

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.


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


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