A Retrospective Trust Region Algorithm with Trust Region Converging to Zero

We propose a retrospective trust region algorithm with the trust region converging to zero for the unconstrained optimization problem. Unlike traditional trust region algorithms, the algorithm updates the trust region radius according to the retrospective ratio, which uses the most recent model information. We show that the algorithm preserves the global convergence of traditional trust region algorithms. The superlinear convergence is also proved under some suitable conditions.