Combined benders partitioning algorithm and multiplier methods for state-constrained discrete optimal control problems

The efficacy of Geoffrion´s taxonomy of large-scale mathematical programming is being investigated in the context of state-constrained optimal control problems. One algorithm which can be synthesized from this taxonomy is called Generalized Benders Decomposition. In this paper, we first consider its direct application to optimal control. Numerical experience indicates the best performance is achieved when the dynamics are non-linear in the control and relatively few state-constraints are violated during the iteration process. To combat this latter difficulty, the algorithm is combined with parametric penalty methods. Some guidelines are provided on how to achieve improved numerical performance using this combined approach.