The LiftOptDyn Package
The LiftOptDyn package also implements the lifting idea described in this SIOPT paper, but is a specialized code for the solution of optimization problems (optimal control, parameter estimation) in the context of dynamic optimization, i.e. problems where cost functional and constraints depend on the solution of a differential equation. From another viewpoint the approach behind LiftOptDyn can be understood as another member of the family of partially reduced direct multiple shooting methods, which have been invented by H.G.Bock and coworkers.
LiftOptDyn currently implements a Gauss-Newton as well as an exact-Hessian SQP method and will be extended to inexact SQP methods in the near future. For the evaluation of the model functions and the solution of the arising initial value problems and the computation of the first and higher-order derivatives of these solutions, LiftOptDyn uses the SolvIND suite. SolvIND contains advanced adaptive integrator codes capable of internal numerical differentiation (IND) as well as various features regarding the reuse of the discretization scheme of the integrator as well as local and global error estimation. These features of SolvIND enable us to use strategies for grid reuse and refreshment that lead to significant reduction of the computational effort needed for integration and sensitivity generation compared to standard integrators. Combining this with the good computational complexity and the other advantages of the lifting approach, LiftOptDyn achieves a very good performance on large-scale dynamic problems with (relatively) few degrees of freedom.