A line search trust-region algorithm with nonmonotone adaptive radius for a system of nonlinear equations

In this paper, a trust‐region procedure is proposed for the solution 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 frameworks as well as decrease the computational cost of the algorithm by decreasing the required number subproblems that must be solved. The global convergence and the local Q‐quadratic convergence rate of the proposed approach are proved. Preliminary numerical results of the proposed algorithm are also reported which indicate the promising behavior of the new procedure for solving the nonlinear system.