New Scaled CG Methods Based on the Newton Direction for Solving Unconstrained Optimization problems

In this paper, we will try to find three positive different values for the scalar . We 1 k used two different ways in our derivations, the first was based on Shannoʹs theorem and the second was based on the descent property of CG-method. We also use Shannoʹs theorem which states that the CG-methods are exactly the BFGS Quasi-Newton method where every step was an approximation to the inverse Hessian matrix and restarted as the identity matrix. In general, our numerical results for (15) test functions with different dimensions indicate that the new scaled CG-method (with its three different versions) performs better than the standard well-known CG methods