# Optimal Control of a Discontinuous Problem

Lukas Adam^{*} and Jiri Outrata

We study an optimal control problem where the constraints are given by an differential equation and a discontinuous time-dependent differential inclusion. After discretizing the problem, we prove convergence of optimal solutions and use the so-called solution map to rewrite the problem as an equivalent one with a complicated composite objective function and simple constraints. Finally, we compute the subdifferential of this new objective function, which allows us to apply a suitable nonsmooth optimization technique to solve the discretized problems. The talk is concluded by an illustrative academic example.

Mathematics Subject Classification: 49J21

Keywords: optimal control; variational inequality; rate independent process; coderivative

Minisymposion: Optimal Control of Time-Dependent Variational Inequalities