Nonmonotone Adaptive Trust-region Method for Nonlinear Equations

The trust region method used to solve the nonlinear programming has been found for last 20 years and is now viewed as an efficient optimization method It is a key channel to solve Maratos effect phenomenon. In this paper an adaptive trust region method with nonmonotone technique for nonlinear equations is proposed and analyzed. The globle method is efficient. Convergence results of the algorithm are established. Numerical results show that the new Algorithm is successful. Therefore, the algorithm in the life sciences, water sciences, earth sciences, engineering and technology, natural sciences and social sciences, such as the economic and financial fields have extensive and important application, therefore, this algorithm has a very good theoretical and practical significance.