Investigation of the Conjugate gradient methods in solving the unconstrained nonlinear optimization problem and its applications

Abstract

In this paper, we consider various types of methods such as; Newton, QuasiNewton, Conjugate gradient, Trust region algorithm and etc. to solve an unconstrained nonlinear optimization problem. in most practical applications, the conjugate gradient method is the most efficient method to solve the large-scale optimization problems. Numerical experimants show that, the conjugate gradient method requires less storage memory compared to that of existing ones. In this paper, we describe the solution of monotone nonlinear equations systems using the conjugate gradient methods.