A New Conjugate Gradient Method for Solving Large Scale Systems of Monotone Equations

Abstract

The conjugate gradient method (CGM) is one of the best algorithms that used to solve and minimize constrained optimization problems. In this work we suggest a new algorithm to solve large-scale nonlinear systems of monotone equations. The suggested method has some advantages such as it doesn't need the Jacobian matrix data nor store matrices at each iteration, also this method can solve large-scale problems. With standard conditions, we established the global convergence for the new method and the numerical experiment shoes that the new method is promised and efficient by comparing with other famous methods.

Keywords: System of monotone equations, Conjugate gradient method and Global convergence.