Efficient Implementations of the Polak–Ribière Conjugate Gradient Algorithm

Abstract

Two modifications of the Polak–Ribière conjugate gradient algorithm are presented. Both modifications eliminate the need for an exact minimization at each iteration and both are shown to be convergent. The advantage of the first modification lies in the fact that it takes less time per iteration than the second modification. However, only the second modification is shown to converge n-step quadratically.