by the a posteriori error estimator for the cost functional of the surrogate model. Thus, the offline phase of the RB method can completely be omitted since the RB model can be adaptively enriched during the outer optimization loop. With this procedure the surrogate model eventually will have a high accuracy around the optimum of the optimization problem, ignoring the accuracy of the part which the outer (and inner) optimization loop does not approach at all. Error aware TR-RB methods can be utilized in many different ways. One possible TR-RB approach has been extensively studied in [@QGVW2017] for linear parametric elliptic equations, which ensures convergence of the nonlocal TR-RB. Note that the experiments in [@QGVW2017] are for up to six dimensional parameter sets without inequality constraints. In [@YM2013], the TR framework is combined with an efficient RB error bound for defining the Trust-Region in the design optimization of vibrating structures using frequency domain formulations. **Main results.** In this contribution we present several significant advances for adaptive Trust-Region Reduced Basis optimization methods for parameterized partial differential equations:

-   For the model function in the TR-RB approach, we follow a non-conforming dual (NCD) approach by choosing as model function the Lagrangian associated 