A new class of three-term double projection approach for solving nonlinear monotone equations

Abstract

Abstract The derivative-free projection methodology is important and highly efficient method to solve large scale monotone equations of nonlinear systems. In this work, we suggested a new class of extensions projection approach employs along with a new line search to show a class of new double projection technique for solving monotone systems of nonlinear equations. Our algorithm can be applied to solve nonsmooth equations, furthermore it’s suitable for large scale equations due to simplicity and limited memory. This method constricts new two appropriate hyperplanes in each point strictly separates xk from the solution set, it can obtain the next iteration x k+1 by projecting xk onto the intersection of two halfspaces and include the solution set of the problem. The global convergence of the given method is investigated with mild assumptions. The numerical experiments prove that the new approach is working well and so promising.