A nonmonotone trust-region-approachwith nonmonotone adaptive radius forsolving nonlinear systems

This paper presents a trust-region procedure for solving systems of non- linear 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 efficiencyand robustness of the trust-region framework as well as can decrease the com- putational cost of the algorithm by decreasing the number of subproblems that must be solved. The global convergence to rst order stationary pointsas 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.

Keywords:

Nonlinear equations , Trust-region framework , Adaptive radius , Nonmonotone technique