Robust Optimization of Large-Sparse Systems

The prevalence of multi-billion-dollar mega-projects have substantially exacerbated the potential risks associated with chemical process safety and environmental failures. The use of model-based approaches to ensure rigorous satisfaction of safety and environmental constraints remains an open area of research within the process systems community [4]. For the general nonlinear case, these problems require the solution of a series of global optimization problems [2,3]. While global optimization techniques exist to address a wide-variety of model-based problems, large-dimensionality systems remain an open-challenge [5]. One approach to mitigate this “curse of dimensionality” is via the reformulation of the problem into a reduced-dimension space via a simulation-based implicit approach. We’re currently investigating the creation of novel fixed-point iteration schemes that will further reduce the computational cost of the methods presented in [1,3] specifically for large-scale physics-based models.



[1] Mitsos, A., Chachuat, B., and Barton, P.I. McCormick-Based Relaxations of Algorithms. SIAM J. Optim. 20(2): 573-601.

[2] Stuber, M.D., Scott, J.K., and P.I. Barton. Convex and Concave Relaxations of Implicit Functions. Optimization Methods and Software. 30(3), 424-460, 2014.

[3] Mitsos, A. Global Optimization of Semi-Infinite Programs via Restriction of the Right-Hand Side. Optimization. 60:10-1,1291-1308, 2011.

[4] Stuber, M.D., and Barton, P.I. Semi-Infinite Optimization with Implicit Functions. Ind. Eng. Chem. Res., 54, 307-317, 2015.

[5] O. Shcherbina, et al. Benchmarking Global Optimization and Constraint Satisfaction Codes, In Global Optimization and Constraint Satisfaction, Bliek, Ch., Jermann, Ch. and Neumaier, A. Springer, Berlin 2003, 212-222.