the quality of the (POD) reduced order model, referred to as TR-POD, a meanwhile well-established method in applications; cf. [@BC08; @CAN12].

TR methods ensure global convergence for locally convergent methods. In each iteration of the TR algorithm the nonlinear objective is replaced by a model function which can be optimized with much less effort; cf. [@CGT00; @NW06]. One suitable choice for the model is a reduced order discretization of the objective (e.g., by utilizing a second-order Taylor approximation). To ensure convergence to stationary points the accuracy of the model function and of its gradient have to be monitored. In [@RoggTV17] a posteriori error bounds are utilized to monitor the approximation quality of the gradient. We also refer to [@GGMRV17], where the authors utilize basis update strategies to improve the reduced order approximation scheme with respect to the optimization goal. The TR strategy can be combined with second-order methods for nonlinear optimization: with the Newton method to solve the reduced problem and with the SQP method for the all-at-once approach; cf. [@HV06].

Constraints on the control and the metric for the Trust-Region radius can affect the convergence of the method. For an error-aware TR method, the TR radius is directly characterized 