Hybridization techniques for the solution of system of nonlinear equations using conjugate gradient method

Abstract

The conjugate gradient method for system of nonlinear equations is rare as most of the methods are for unconstrained optimization and may not necessarily generate sufficient descent or descent direction. Most of the current studies are on the New Hybrid Algorithm for Convex Nonlinear Unconstrained Optimization. This paper presents an effective conjugate gradient method via hybridization techniques for the solution of system of nonlinear equations. The study aimed to use hybridization techniques to solve system of nonlinear equations using conjugate gradient methods. And the study is to achieve these objectives; to derive methods that are derivative free, to present an effective conjugate gradient method, to present methods with sufficient descent direction. We achieved these by hybridizing some well-known conjugate gradient methods. The scheme satisfies the sufficient decent condition. Under mild condition, the global convergence result for the method is established. Preliminary numerical results for some large-scale benchmark test problems reported in this work, demonstrate that, the method is practically effective and competitive to some existing methods. This study have applications in engineering such as structural engineering, mechanical engineering, electrical and electronic engineering, applied mathematics and numerical analysis, computer science and machine learning etc. in solving system of nonlinear equations using the conjugate gradient method which is fast and efficient.