Combinatorial Integral Approximation Decompositions for Mixed-Integer Optimal Control

Solving mixed-integer nonlinear programs (MINLPs) is hard from both a theoretical and practical perspective. Decomposing the integer part promising computational point of view. In general, however, no bounds on objective value gap can be established iterative procedures with potentially many subproblems are necessary. The situation different for optimal control problems binary variables that switch over time. Here, priori were derived decomposition into one continuous problem linear program, combinatorial integral approximation (CIA) problem. this article, we generalize extend idea. First, derive decompositions analyze implied bounds. Second, propose several strategies to recombine candidate solutions functions in original We present extensions ordinary differential equations-constrained problems. These transferable straightforward way, though, recently suggested variants certain partial equations, algebraic additional constraints, discrete time implemented all algorithms AMPL proof-of-concept study. Numerical results show improvement compared standard CIA respect function general-purpose MINLP solvers runtime.