Automatic determination of an initial trust region in nonlinear programming

This paper presents a simple but efficient way to find a good initial trust region radius in trust region methods for nonlinear optimization. The method consists of monitoring the agreement between the model and the objective function along the steepest descent direction, computed at the starting point. Further improvements for the starting point are also derived from the information gleaned during the initializing phase. Numerical results on a large set of problems show the impact the initial trust region radius may have on trust region methods behaviour and the usefulness of the proposed strategy.