New properties of a nonlinear conjugate gradient method

Summary.

This paper provides several new properties of the nonlinear conjugate gradient method in [5]. Firstly, the method is proved to have a certain self-adjusting property that is independent of the line search and the function convexity. Secondly, under mild assumptions on the objective function, the method is shown to be globally convergent with a variety of line searches. Thirdly, we find that instead of the negative gradient direction, the search direction defined by the nonlinear conjugate gradient method in [5] can be used to restart any optimization method while guaranteeing the global convergence of the method. Some numerical results are also presented.