Another hybrid conjugate gradient algorithm for unconstrained optimization

Another hybrid conjugate gradient algorithm is subject to analysis. The parameter k is computed as a convex combination of HS k (Hestenes-Stiefel) and DY k (Dai-Yuan) algorithms, i.e. (1 )C HS k k k k DY k = - + . The parameter k in the convex combination is computed in such a way so that the direction corresponding to the conjugate gradient algorithm to be the Newton direction and the pair to satisfy the quasi-Newton equation( , )k ks y 2 1( )k k kf x s y+ = k, where and1k ks x x+= - 1 .k k ky g g+= - The algorithm uses the standard Wolfe line search conditions. Numerical comparisons with conjugate gradient algorithms show that this hybrid computational scheme outperforms the Hestenes-Stiefel and the Dai-Yuan conjugate gradient algorithms as well as the hybrid conjugate gradient algorithms of Dai and Yuan. A set of 750 unconstrained optimization problems are used, some of them from the CUTE library. MSC: 49M07, 49M10, 90C06, 65K

• Type: Journal
• Year: 2008
• Where: NA
• Authors: Neculai Andrei
• Keywords: Algorithms, Conjugate Gradient Algorithm, Gradient, NA 2008