In this talk, we address the optimization of complex parameter-dependent systems relevant for many real world problems like autonomous driving. We focus on a function approximation approach for the arising parametric optimization problems. Building upon our work [DeMarchi22], the approach aims at finding an approximation function that maps a parameter to the solution of the corresponding parametric optimization problem. For this, we derive the corresponding Karush-Kuhn-Tucker (KKT) equations. By exploiting the Fischer-Burmeister function, the derived necessary optimality conditions can be reformulated as a nonlinear system of equations. For given training parameters, this nonlinear system is used to define an objective function to train an approximating function to output the corresponding KKT points. Thereby, the approximating function can take different forms. For instance, our theoretical results from [DeMarchi22] are tailored to an approximation by radial basis functions. In the first part of this talk, we show how these results can be extended to neural networks and discuss current trends in this field. More precisely, we show under which conditions the training of the neural network leads to an approximation function for KKT points and prove error bounds for system parameters, which are not part of the training set. In the second part of this talk, we show how the above introduced approach can unleash its full potential in the field of optimal control. For instance, we show how it can be used in hierarchical approaches [Gottschalk24] as well as in the classical model predictive control setting. In both cases, it can replace the time-consuming process of solving an optimal control problem by instead just executing the approximation function once. This accelerates computing the control strategy for various parameters and can lead to a real-time capability for complex tasks. We illustrate the entire framework using the application example of a car on a race track.