- - - Master of Mathematics, Technical Institute of Kirkuk, Northern Technical University, Iraq

In this paper, an efficient GV۱-CG is developed to optimizing the modified conjugate gradient algorithm by using a new conjugate property. This is to to increase the speed of the convergence and retain the characteristic mass convergence using the conjugate property. This used property is proposed to public functions as it is not necessary to be a quadratic and convex function. The descent sharp property and comprehensive convergence for the proposed improved algorithm have been proved. Numerical results on some test function indicate that the new CG-method outperforms many of the similar methods in this field.

Conjugate gradient, Developed conjugation property, Improved algorithm, Optimization, Global convergence, Descent Direction