A nonlinear conjugate gradient method based on the MBFGS secant condition

In this article, a new conjugate gradient method based on the MBFGS secant condition is derived, which is regarded as a modified version of Dai-Liao method or Yabe-Takano method. This method is shown to be globally convergent under some assumptions. It is new feature that the proof of global convergence of this method is very simple without proving so-called Property (*) given by Gilbert and Nocedal for general unconstrained optimization problems. Our numerical results show that this method is efficient for the given test problems.