A New Scalar of Conjugate Gradient Methods for Solving Unconstrained Minimization

In this paper, we derive a search direction for the conjugate-gradient method based on the use of the self-scaling Quasi Newton-method, and the usefulness of the new method is to solve unconstrained optimization problems with large dimensions. To clarify the importance of the proposed method, we have shown its characteristics in terms of the sufficient descent condition and the theoretically global convergence condition. Numerically, we applied the proposed method to a variety of known test functions to prove its effectiveness. When compared with some previous methods in the same direction, the proposed method proved to be superior to them that the tools used for this purpose.