the offline phase, whereas evaluating the ROM is called online phase.

There exists a large amount of literature using such reduced order surrogate models for optimization methods. A posteriori error estimates for reduced approximation of linear-quadratic optimization problems and parametrized optimal control problems with control constraints were studied, e.g., in [@Dede2012; @GK2011; @KTV13; @NRMQ2013; @OP2007]. In [@dihl15] an RB approach is proposed which also enables an estimation on the actual error on the control variable and not only on the gradient of the output functional. Certified Reduced Basis methods for parametrized elliptic optimal control problems with distributed controls were studied in [@KTGV2018]. With the help of an a posteriori error estimator, ROMs can be constructed with respect to a desired accuracy but also with respect to a local area in the parameter set [@EPR2010; @HDO2011]. For very high dimensional parameter sets, simultaneous parameter and state reduction has been advised [@HO2014; @HO2015; @LWG2010]. However, constructing a reduced order surrogate for a prohibitively expensive forward problem can also take a significant amount of computational resources. To remedy this, it is beneficial to use optimization methods that optimize on a local level of the control variable, assuming the surrogate only to be accurate 