A NEW  CONJUGATE GRADIENT WITH GLOBAL CONVERGES FOR NONLINEAR PROBLEMS

SALAH GAZI  SHAREEF

doi:10.26682/sjuod.2022.25.2.51

SALAH GAZI SHAREEF Dept. of Mathematics, Faculty of Science, University of Zakho, Kurdistan Region-Iraq

DOI: https://doi.org/10.26682/sjuod.2022.25.2.51

Keywords: Nonlinear Optimization, Algorithm of Conjugate Gradient, property of the Descent, property of the Sufficient Descent and Global Converges Properties

Abstract

The conjugate gradient(CG) method is one of the most popular and well-known iterative strategies for solving minimization problems, it has extensive applications in many domains such as machine learning, neural networks, and many other fields, partly because to its simplicity in algebraic formulation and implementation in codes of computer and partially due to their efficiency in solving large scale unconstrained optimization problems. Fletcher/Reeves (C, 1964) expanded the concept to nonlinear problems. In 1964, and this is widely regarded as the first algorithm of nonlinear conjugate gradient. Since then, other conjugate gradient method versions have been proposed. In this paper and in section one, we derive a new conjugate gradient for solving nonlinear minimization problems based on parameter of Perry. In section two we will satisfy some conditions like descent and sufficient descent conditions. In section three , we will study the global convergence of new suggestion. We present numerical findings in the fourth part to demonstrate the efficacy of the suggestion technique. Finally, we provide a conclusion

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