New conjugacy condition with pair-conjugate gradient methods for unconstrained optimization

Conjugate gradient methods are wildly used for unconstrained optimization especially when the dimension is large. In this paper we propose a new kind of nonlinear conjugate gradient methods which on the study of Dai and Liao (2001), the new idea is how to use the pair conjugate gradient method with this study (new cojugacy condition) which consider an inexact line search scheme but reduce to the old one if the line search is exact. Convergence analysis for this new method is provided. Our numerical results show that this new methods is very efficient for the given ten test function compared with other methods.