A new hybrid conjugate gradient method as a convex combination methods

Abstract

The conjugate gradient (CG) method is a widely employed algorithm for solving large-scale unconstrained optimization problems due to its fast convergence and efficient memory usage. In this paper, we suggest a new hybrid nonlinear conjugate gradient method, which the conjugate gradient coefficient β_k is a convex combination of β_k^NPRP  and β_k^DY  . The parameter θ_k is computed in such a way that the conjugacy condition is satisfied. With the strong Wolfe line search, the descent property and global convergence of the new hybrid method are proved. The numerical results also show that our method is robust and efficient.