On Convergence and Restart Conditions for a Nonlinear Conjugate Gradient Method

A global convergence theorem for unconstrained minimization algorithms with an eecient line search is derived. The theorem applies to a new version of the conjugate gradient method derived here in terms of minimizing the eeect of zigzagging. The global convergence condition makes much weaker demands on the line search than previous methods. Local Q-linear convergence in a neighborhood of a strong local minimizer follows under additional conditions that deene natural restart conditions based on line search accuracy and loss of conjugacy of successive gradients.