On Efficiency of Non-Monotone Adaptive Trust Region and Scaled Trust Region Methods in Solving Nonlinear Systems of Equations

In this paper we run two important methods for solving some well-known problems and make a comparison on their performance and efficiency in solving nonlinear systems of equations. One of these methods is a non-monotone adaptive trust region strategy and another one is a scaled trust region approach. Each of methods showed fast convergence in special problems and slow convergence in other ones; we try to categorize these problems and find out that which method has better numerical behavior. The robustness of methods is demonstrated by numerical experiments.