A new self-adaptive rule of trust region radius is introduced, which is given by a piecewise function on the ratio between the actual and predicted reductions of the objective function. A self-adaptive trust region method for unconstrained optimization problems is presented. The convergence properties of the method are established under reasonable assumptions. Preliminary numerical results show that the new method is significant and robust for solving unconstrained optimization problems.
"A Novel Self-Adaptive Trust Region Algorithm for Unconstrained Optimization." J. Appl. Math. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/610612