Abstract
There have been some conjugate gradient methods with strong convergence but numerical instability and conversely. Improving these methods is an interesting idea to produce new methods with both strong convergence and numerical stability. In this paper, a new hybrid conjugate gradient method is introduced based on the Fletcher formula (CD) with strong convergence and the Liu and Storey formula (LS) with good numerical results. New directions satisfy the sufficient descent property, independent of line search. Under some mild assumptions, the global convergence of new hybrid method is proved. Numerical results on unconstrained CUTEst test problems show that the new algorithm is very robust and efficient.