New conjugacy conditions and related nonlinear conjugate gradient methods

Conjugate gradient methods are a class of important methods for unconstrain ed optimization, especially when the dimension is large. This paper propose s 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 co njugacy condition, two nonlinear conjugate gradient methods are constructed . Convergence analysis for the two methods is provided. Our numerical resul ts show that one of the methods is very efficient for the given test proble ms.