A New Search Direction via Hybrid Conjugate Gradient Coefficient for Solving Nonlinear System of Equations

Abstract

Conjugate gradient methods are widely used for unconstrained optimization problems. Most of the conjugate gradient methods do not always generate a descent search direction. In this article, a new search direction via hybrid conjugate gradient method by convex combination of the earlier works is used and extended for the solution of nonlinear system of equations. The proposed search direction generates a descent direction at every iteration and without convexity assumption on the objective function. The new method possesses, preserved and inherits the properties of the Conjugate Gradient (CG) coefficient used. The proposed hybridized method played a useful, vital and powerful role in solving large-scale nonlinear system of equations as indicated in the numerical results.