Convergence Of The New Descent Conjugate Gradient Methods

Our paper including three sections. We prove convergence of the conjugate gradient methods. then we give the properties of the new methods with the modified secant condition.In the first section, we introduce the development of the conjugate gradient methods.In the second section, we propose a new conjugate gradient method following to the method presented by Hager and Zhang (2005). and we give the similar convergence theorems. our numerical results show that the new conjugate gradient methods are feasible.In the third section, we proposed another conjugate gradient method following to the method presented in the first section with the modified secant condition. this method has the second-order curvature of the objective function and achieves a high-order accuracy. then We prove convergence of the conjugate gradient methods.