A nonmonotone trust-region-approach with nonmonotone adaptive radius for solving nonlinear systems

This paper presents a trust-region procedure for solving systems of nonlinear equations. The proposed approach takes advantages of an effective adaptive trust-region radius and a nonmonotone strategy by combining both of them appropriately. It is believed that selecting an appropriate adaptive radius based on a suitable nonmonotone strategy can improve the efficiency and robustness of the trust-region framework as well as can decrease the computational cost of the algorithm by decreasing the number of subproblems that must be solved. The global convergence to first order stationary points as well as the local q-quadratic convergence of the proposed approach are proved. Numerical experiments show that the new algorithm is promising and attractive for solving nonlinear systems.