A retrospective trust-region method for unconstrained optimization (Q964178)

The authors introduce a natural variant of the basic trust-region algorithm, where the most recent model information at the current iterate (rather than at the preceding one) is exploited to update the trust-region radius. The update is then performed according to how well the current model retrospectively predicts the value of the objective function at last iterate. It is also shown that limit points of sequences of iterates produced by the new algorithm are second-order critical points for the minimization problem. The preliminary numerical experiments indicate that the method is advantageous when the model is good, and its quality is exploited by an accurate subproblem solution. This new model is especially interesting for adaptive techniques for noisy functions. The potential of the new approach is to exploit the most recent information on the noise to improve numerical performance.