A derivative-free scaling memoryless DFP method for solving large scale nonlinear monotone equations.

Quasi-Newton methods for solving nonlinear system of equations provide an attractive alternative to the Newton method in which they do not require computation of the Jacobian matrix and still possess superlinear convergence. In this paper, we develop a new sufficient descent direction based on a scaling memoryless DFP updating formula. By combining this descent direction with a projection approach, we propose a derivative-free scaling memoryless DFP method for solving nonlinear monotone equations and establish its global convergence under reasonable conditions. In sharp contrast with the original DFP method, our new method does not involve computing matrices. This makes it particularly suitable for solving large scale problems. The presented results of numerical experiments demonstrate the robustness and efficiency of our new method. [ABSTRACT FROM AUTHOR]