  Models involving hybrid systems are versatile in their application, but
difficult to handle and optimize efficiently due to their combinatorial nature.
This work presents a method to cope with hybrid optimal control problems which,
in contrast to decomposition techniques, does not require relaxing the
integrality constraints. Based on the discretize-then-optimize approach, our
scheme addresses mixed-integer nonlinear problems under mild assumptions. The
proposed numerical algorithm builds upon the augmented Lagrangian framework,
whose subproblems are handled using successive mixed-integer linearizations
with trust regions. We validate the performance of the numerical routine with
extensive investigations using several hybrid optimal control problems from
different fields of application. Promising preliminary results are presented
for a motion planning task with hysteresis and drag, a Lotka-Volterra fishing
problem, and a facility location design problem.
