Figure 1.

Solution Strategy. The system of ODEs is first reformulated into a nonconvex NLP using the orthogonal collocation on finite elements approach. This NLP is decomposed into two levels: a master MILP and a slave NLP. The master MILP, which is constructed using piecewise McCormick envelopes and supporting hyper-planes, provides a rigorous lower bound on the global optimum. The slave NLP corresponds to the original nonconvex NLP that is solved using as starting point the solution of the MILP. The algorithm iterates between these two levels until the optimality gap (i.e., the relative difference between the upper and lower bounds) is reduced below a given tolerance.