Using a New Trust Region Algorithm with Nonmonotone Adaptive Radius for Solving Nonlinear Systems of Equations

Abstract

In this work, we present a new method to solve nonlinear systems of nonmonotone equations by combining the trust region method (TRM) with nonmonotone technique. The new method will solve the nonlinear system with less time and effort by introducing a new radius of nonmonotone trust region radius (TRR). We will show that the new technique is good to solve many problems. The global convergence of the new algorithm is established, the numerical results are calculating and we compared them with other algorithms in terms of time and function evaluation and the number of iteration, the numerical result tells us that the new method is the best.

Keywords: Trust region method· Global convergence. Nonlinear equations.