A new projection technique for developing a Liu-Storey method to solve nonlinear systems of monotone equations

Abstract

The projection technique is a very important method and efficient for solving unconstraint optimization and nonlinear equations. In this study, we developed a Liu-Story (LS) algorithm for solving monotone equations of nonlinear systems. The new algorithm satisfies the sufficient descent condition and it’s a suitable method of large scale equations for its limited memory. We established a global convergence of suggest method under the mild conditions. Numerical results proved that the new algorithm works well and promising.