Mathematical modeling of dynamic processes in science and engineering
frequently leads to large systems of differential-algebraic equations (DAE) or partial differential-algebraic equations (PDAE),
which are used in process simulation. Typically, these mathematical models involve unknown model parameters that have to be fitted against experimental data to ensure a good match between mathematical model and reality.
For the solution of such problems, boundary value problem (BVP) methods
with multiple shooting or collocation discretization have proven to be very
The basic idea is to treat the discretized DAE model as
a nonlinear constraint of the optimization problem. This problem is then
solved by algorithms that allow infeasible points, such as generalized
Gauss-Newton or SQP methods.