06031709

j

06031709 Zhang, Yang Wang, Kairong A new general form of conjugate gradient methods with guaranteed descent and strong global convergence properties. Numer. Algorithms 60, No. 1, 135-152 (2012). 2012 Springer, Dordrecht EN conjugate gradient method line search sufficient descent condition global convergence Polak-Ribi\`ere-Polyak Hestenes-Stiefel Liu-Storey Dai-Yuan-type conjugate-descent-type numerical results

doi:10.1007/s11075-011-9515-0

The authors present a new general form of conjugate gradient methods and give a sufficient condition for the global convergence of the proposed method under weak conditions on the objective function. They also establish a variety of convergence results on other conjugate gradient methods, which include the Polak-Ribi\`ere-Polyak, Hestenes-Stiefel, Liu-Storey, Dai-Yuan-type and Conjugate-Descent-type methods. Some preliminary numerical results are provided. Guoqiang Wang (Shanghai)