Algorithm 851: CG DESCENT, a conjugate gradient method with guaranteed descent

Recently, a new nonlinear conjugate gradient scheme was developed which satisfies the descent condition g(k)(inverted perpendicular)dk <= - 7/8 parallel to g(k)parallel to(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.