Algorithm 851

Recently, a new nonlinear conjugate gradient scheme was developed which satisfies the descent condition g T k d k ≤ −7/8 ‖ g k ‖ 2 and which is globally convergent whenever the line search fulfills the Wolfe conditions. This article studies the convergence behavior of the algorithm; extensive numerical tests and comparisons with other methods for large-scale unconstrained optimization are given.