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Optimization Theory and Algorithms

An effective way of incorporating uncertainty in optimization formulations is to use a two-stage stochastic programming approach, in which multiple scenarios corresponding to uncertainty realizations are embedded within a single optimization formulation. However, the already large- scale dynamic optimization problems typical of complex industrial systems becomes significantly amplified with an increasing number of scenarios. We developed within MACC a novel parallel computing approach for solving large-scale dynamic optimization problems problems of this type. It utilizes a multiple-shooting method for integration of the differential- algebraic equation (DAE) system, in which the time horizon is partitioned into a number of intervals, with the initial states in each interval treated as optimization decision variables. The integration over the intervals for the various scenarios can thus be treated as independent integration tasks, suitable for distribution to multiple processors. Our work includes parallelization of the nonlinear programming solution through sequential quadratic programming with parallel solution of the quadratic programming subproblems.

Dr. Chris L. E. Swartz
Professor and Director, MACC
Dr. Thomas A. Adams II
Associate Professor
Dr. Kamil A. Khan
Assistant Professor
Huiyi Cao
Ph.D. Candidate
Madison Glover
M.A.Sc. Candidate
Chiral Mehta
M.A.Sc. Candidate
Yingkai Song
Ph.D. Candidate
Yingwei Yuan
M.A.Sc. Candidate
Whitney differentiability of optimal-value functions for bound-constrained convex programs
Optimization, 68 691-711 (2019)  -  [ Publisher Version ]
Convergence of Subtangent-Based Relaxations of Nonlinear Programs
Processes, 7 (4) 221 (2019)  -  [ Publisher Version ]
Subtangent-based approaches for dynamic set propagation
IEEE Conference on Decision and Control, 17-19 (2018)  -  [ Publisher Version ]
Global optimization of MIQCPs with dynamic piecewise relaxations
Castillo, P., Castro, Pedro, Mahalec, V.
Journal of Global Optimization, 71 (4) 691-716 (2018)  -  [ Publisher Version ]
Branch-locking AD techniques for nonsmooth composite functions and nonsmooth implicit functions
Optimization Methods and Software, 33 1127-1155 (2018)  -  [ Publisher Version ]
A parallel structure exploiting nonlinear programming algorithm for multiperiod dynamic optimization
Computers & Chemical Engineering, 103 151-164 (2017)  -  [ Publisher Version ]
Multi-Period Dynamic Optimization for Large-Scale Differential-Algebraic Process Models under Uncertainty
Processes, 3 (3) 541-567 (2015)  -  [ Publisher Version ]
Design under uncertainty using parallel multi-period dynamic optimization
AIChE Journal (2014)  -  [ Publisher Version ]