A MODIFICATION OF HYBRID CONJUGATE GRADIENT METHOD BASED ON MEMORYLESS BROYDEN'S UPDATE FOR NONLINEAR SYSTEMS OF EQUATIONS

ABSTRACT Conjugate Gradient (CG) methods are widely used for solving large-scale nonlinear systems of equations due to their efficiency in employing vector operations. Many articles developed different kinds of conjugate gradient coefficients. Recently, some conjugate gradients were proposed with large dimensions, but they have small sample sizes. So, they cannot solve problems that have higher dimensions. In this research, we propose a novel hybrid conjugate gradient method for nonlinear system of equations. The parameter is computed as a convex combination of and coefficients respectively. It satisfies a sufficient descent and converge globally under some suitable conditions. Numerical results of the hybrid algorithm show effectiveness in large scale unconstrained optimization problems. Keywords: Hybrid Conjugate Gradient, Wolfe line search, Global Convergence Analysis.