Scaled three-term derivative-free methods for solving large-scale nonlinear monotone equations

In this paper, two effective derivative-free methods are proposed for solving large-scale nonlinear monotone equations, in which the search directions are sufficiently descent and independent of the line search. The methods are the extensions of the conjugate gradient methods proposed by Bojari and Eslahchi (Numer. Algorithms 83, pp. 901–933, 2020) combined with the hyperplane projection technique. Our approaches are low storage memory and derivative-free, which makes them suitable for large-scale nonsmooth monotone nonlinear equations. Under proper assumptions, we analyze the global convergence property of the proposed methods. Finally, numerical experiments show that the proposed methods outperform some existing ones.