Bulletin of the
Korean Mathematical Society BKMS

In this paper, an efficient hybrid nonlinear conjugate gradient method is proposed to solve general unconstrained optimization problems on the basis of CD method \cite{3} and DY method \cite{4}, which possess the following property: the sufficient descent property holds without any line search. Under the Wolfe line search conditions, we proved the global convergence of the hybrid method for general nonconvex functions. The numerical results show that the hybrid method is especially efficient for the given test problems, and it can be widely used in scientific and engineering computation.

Keywords: unconstrained optimization, conjugate gradient method, the Wolfe line search, descent property, global convergence

MSC numbers: 46N10