New properties of a nonlinear conjugate gradient method

This paper provides several new properties of the nonlinear conjugate gradi ent method in [5]. Firstly, the method is proved to have a certain self-adj usting property that is independent of the line search and the function con vexity. Secondly, under mild assumptions on the objective function, the met hod is shown to be globally convergent with a variety of line searches. Thi rdly, we find that instead of the negative gradient direction, the search d irection defined by the nonlinear conjugate gradient method in [5] can be u sed to restart any optimization method while guaranteeing the global conver gence of the method. Some numerical results are also presented.