A Nonlinear Conjugate Gradient Method without Line Search and Its Global Convergence

Based on the method of Sun and Zhang (2001), we present a conjugate gradient method without line search. At each iteration, the step size is determined by a formula, which does not involve any matrix and uses both available function value and gradient information. Under mild assumptions, we prove that the proposed method has global convergence if the parameter is computed by five well-known formulae given by Feltcher-Reeves, Polak-Ribiere, Hestenses-Stiefel, Dai-Yuan and the conjugate descent method.