Parametric sensitivities for optimal control problems using automatic differentiation

This article presents a new area of application for Automatic Differentiation (AD): Computing parametric sensitivities for optimization problems. For an optimization problem containing parameters which are not among the optimization variables, the term parametric sensitivity refers to the derivative of an optimal solution with respect to the parameters. We treat non-linear finite- and infinite-dimensional optimization problems, in particular optimal control problems involving ordinary differential equations with control and state constraints, and compute their parametric sensitivities using AD. Particular attention is given to the generation of second-order derivatives required in the process.