A New Scalar of Conjugate Gradient Methods for Solving Unconstrained Minimization

Abstract

In this paper, we derive a search direction for the conjugate-gradient method based on use of self-scaling Quasi Newton-method, and the usefulness of the new method is to solve unconstrained optimization problems with large dimensions. In order 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 of the same direction, the proposed method proved to be superior to them in relation to the tools used for this purpose.