Many problems in economy and industry require an optimal solution under consideration of specific criteria and constraints. From a mathematical point of view, this requires the numerical solution of a parametric optimization problem or a dynamic optimization problem. The latter formulation accounts for the dynamics of the underlying process and is particularly relevant in the context of optimal control and model predictive control (MPC). In summary, the course covers the following topics:

• Introduction to and examples of static and dynamic optimization problems
• Unconstrained numerical optimization (optimality conditions, numerical methods)
• Constrained numerical optimization (linear/quadratic/nonlinear problems, optimality conditions, numerical methods)
• Dynamical optimization / optimal control problems (calculus of variations, optimality conditions, PMP, numerical methods)
• Nonlinear model predictive control (formulations, stability, real-time solution)