Large-scale Nonlinear Programming: An Integrating Framework for Enterprise-Wide Dynamic Optimization

Integration of real-time optimization and control with higher level decision making (scheduling and planning) is an essential goal for profitable operation in a highly competitive environment. While integrated large-scale optimization models have been formulated for this task, their size and complexity remains a challenge to many available optimization solvers. On the other hand, recent development of powerful, large-scale solvers leads to a reconsideration of these formulations, in particular, through development of efficient large-scale barrier methods for nonlinear programming (NLP). As a result, it is not unrealistic to solve NLPs on the order of a million variables, for instance, with the IPOPT algorithm. More recently, IPOPT has been embodied as an object oriented code that exploits problem structure, takes advantage of parallelism, and allows configuration of different "internal decomposition strategies" without compromising its fast convergence properties. Finally, an NLP sensitivity extension was added to this code that allows the fast approximate solution of perturbed NLP problems. These developments are demonstrated on dynamic optimization formulations that integrate real-time optimization with on-line calculations required by model predictive control. This allows on-line computations to be drastically reduced, even when large nonlinear optimization models are considered.