Scalable mathematical optimization under uncertainty with applications to extreme-scale energy systems
Cosmin G. Petra, Ph.D.
Mathematics and Computer Science Division
Argonne National Laboratory
Monday – March 28, 2016
10:00a.m. – 11:30a.m.
S&E II, Rm. 302
View candidate's talk live here
Stochastic optimization is a leading mathematical paradigm for the optimal control, optimal design, economic and reliable operation, and long-term planning of complex systems under uncertainty. For large scale systems and large uncertainty spaces, stochastic optimization problems can reach extreme sizes (e.g., billions of decision variables and constraints). Scalable algorithms and high-performance computing (HPC) are therefore crucial when solving these problems. In this talk, I will present a computational framework for stochastic optimization on HPC platforms (PIPS). PIPS uses interior-point numerical optimization methods and specialized, distributed memory linear algebra obtained based on a Schur complement decomposition. I will focus on the mathematical algorithms and analysis that enabled solving stochastic problems of unprecedented sizes arising in the economic optimization of electricity dispatch for the State of Illinois. Performance and efficiency metrics of the algorithms and implementations on various HPC architectures will be discussed. Often stochastic optimization problems have dynamic constraints described by differential-algebraic equations (DAEs), as is the case with optimal control and parameter and state estimation for power grid. Motivated by the unavailability of second-order derivatives for dynamic constraints in real-world problems, in the second part of my talk I will propose and analyze a novel structured quasi-Newton optimization algorithm that builds secant Hessian approximations for the dynamic constraints and reuses the existing second-order derivatives. The algorithm is aimed at reducing the performance gap between pure Newton and plain quasi-Newton optimization methods and is a key step for scalable dynamic optimization.
Cosmin Petra is an assistant computational mathematician in the Mathematics and Computer Science Division at Argonne National Laboratory. He received his B.Sc. degree in Mathematics and Computer Science from Babes-Bolyai' University, Romania, and his M.S. and Ph.D. degrees in Applied Mathematics from the University of Maryland, Baltimore County. His research interests lie at the intersection of numerical optimization, scalable algorithms for extreme-scale problems, and high-performance scientific computing, with a focus on the optimization of complex energy systems under uncertainty.