Three terms of derivative free projection technique for solving nonlinear monotone equations

Abstract

The derivative-free projection technique is one of the efficient methods for solving nonlinear monotone equations. In this study, three terms of the derivative-free projection method with a monotone line search technique is presented. This method based on extension of a conjugate gradient descent and a developed gradient projection method to solve the nonlinear system of monotone equations. The proposed method can be used for large scale equations due to limited memory requirement. We investigated the global convergence of the suggested approach without requiring differentiability and also the equation is Lipschitz continuous. The numerical results showed that the new algorithm is efficient and promised.