Sharif Digital Repository

Conjugate gradient methods are appealing for large scale nonlinear optimization problems, because they avoid the storage of matrices. Recently, a new conjugacy condition proposed by Dai and Liao, considers an inexact line search scheme that reduces to the old one if the line search is exact. Based on this condition, a new conjugate gradient method was proposed that has fast convergence. Later, Yabe and Takano, based on new conjugacy condition and modified secant condition, proposed another conjugate gradient method. This method takes both the available gradient and function value information and achieves a high-order accuracy in approximating the second-order curvature of the objective...