Algorithm 85: CG_DESCENT, a Conjugate Gradient Method with Guaranteed Descent

摘要

Recently, a new nonlinear conjugate gradient scheme was developed which satisfies the descent condition g_k~T 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.