ON THE USE OF POWELL'S RESTART STRATEGY TO CONJUGATE GRADIENT METHODS

Restart strategy is often used in conjugate gradient (CG) methods to improve their computational efficiency. In this paper, we propose to apply Powell's restart strategy [20] to four classical CG methods including the Fletcher-Reeves (FR) method [10], the Polak-Ribiere-Polyak (PRP) method [18,19], the Hestenes-Stiefel (HS) method [15], and the Dai-Yuan (DY) method [6]. We show that the corresponding variants of all aforementioned CG methods enjoy the sufficient descent property and are globally convergent if a generalized improved Wolfe line search is performed. Numerical results show that the use of Powell's restart strategy to the four classical CG methods can significantly improve their computational efficiency. In particular, the numerical performance of the corresponding variant of the HS method compares favorably with the one of the Dai-Kou's CGOPT in [3].