A Dai-Yuan conjugate gradient algorithm with sufficient descent and conjugacy conditions for unconstrained optimization

A modification of the Dai-Yuan conjugate gradient algorithm is proposed. Using the exact line search, the algorithm reduces to the original version of the Dai and Yuan computational scheme. For inexact line search the algorithm satisfies both the sufficient descent and conjugacy condition. A global convergence result is proved when the Wolfe line search conditions are used. Computational results, for a set consisting of 750 unconstrained optimization test problems, show that this new conjugate gradient algorithm substantially outperforms the Dai and Yuan conjugate gradient algorithm and is close to its hybrid variants. MSC: 49M07, 49M10, 90C06, 65K