A new hybrid scaling parameter for a VM-algorithm

In this paper we have proposed a modified hybrid conjugate direction algorithm which combined a well-known CG-method which was based on a non-quadratic model and a well-known VM-method which based on the quadratic model.The new modified algorithm was treated both theoretically and numerically and proved to be stable and its convergence was super-linear and it uses an exact line search.Our numerical results indicate that the modified hybrid method performs well compared to the two well-known used method.