A modified HS projection method for solving large scale nonlinear monotone equations

In order to overcome the shortcomings of other algorithms such as their complexity, programming difficulty and the large storage, and so on, and to solve efficiently large scale nonlinear monotone equations, a new search direction was put forward based on the traditional HS algorithm. Meanwhile, the HS projection method was modified by the projection technique and the search approach. The new algorithm had the sufficient descent property and trust region features without any line searches. Under some mild assumptions, the global convergence was proved. The numerical calculation results showed that the new algorithm was more excellent and had the better robustness comparing with traditional HS algorithm and Three tern HS algorithm. The new algorithm was more efficient for solving large scale nonlinear monotone equations.