  We are considering differential-algebraic equations with embedded
optimization criteria (DAEOs) in which the embedded optimization problem is
solved by global optimization. This actually leads to differential inclusions
for cases in which there are multiple global optimizer at the same time. Jump
events from one global optimum to another result in nonsmooth DAEs and thus
reduction of the convergence order of the numerical integrator to first-order.
Implementation of event detection and location as introduced in this work
preserves the higher-order convergence behavior of the integrator. This allows
to compute discrete tangents and adjoint sensitivities for optimal control
problems.
