Using a New Projection Approach to Find the Optimal Solution for Nonlinear Systems of Monotone Equation

Abstract

There are many algorithms are used to solve systems of nonlinear monotone equations with various advantages and disadvantages, including the line search algorithm, trust region algorithm, projection algorithm and others. In this paper we used a new projection algorithm to solve these systems. The projection methods are considered one of the effective free derivative methods to solve systems of nonlinear monotone equations. The framework of this method is that the current iterate is separated strictly from the solution set of the problem in each iteration by a suitable hyperplane which constructs by the new algorithm. Then, in order to determine the new approximation, the current iteration is projected on this hyperplane. The global convergence of the proposed algorithm is proven under standard assumptions. The numerical results showed that the suggested algorithm is very efficiency and promising.