Improved Computational Performance of a Modified Conjugate Gradient Coefficient for Solving Nonlinear System of Equations

Abstract

Conjugate gradient (CG) method is an evolution of computational method in solving optimization problems. The aim of this research is to improve the computational performance of an existing conjugate gradient parameter. In this article, an existing conjugate gradient coefficient is considered, and its computational performance is improved using a derivative free line search. The computational performance is based on number of iteration and the CPU time it take to solve a particular problem. Numerical results was implemented using some benchmark problems coded using MATLAB and run on a personal computer 2.4GHz, Intel (R) Core (TM) i7-5500U CPU processor, 4GB RAM memory and on an Acer Aspire with a Windows 7 operating system. The two methods are compared numerically on Microsoft excel 2016.  The approach is easy to implement due to its derivative-free nature. It shows that the proposed method is efficient and accurate, thereby appropriate for solving large-scale nonlinear system of equations.