Rigorous Systems Research Group (RSRG) Seminar
Global Optimization by means of Parabolic Relaxation
We introduce convex relaxations and numerical algorithms with an unprecedented level of scalability, (i) to accommodate nonconvex polynomials, (ii) integer variables, and (iii) nonlinear learning models. In lieu of local search algorithms, computationally demanding relaxations, and linearization techniques, we pursue a novel approach, namely "parabolic relaxation," which is fundamentally more efficient compared to the state-of-the-art methods for nonlinear optimization. The ability of parabolic relaxation in finding globally optimal points is manifested on a number of long-standing NP-hard problems in power systems and optimal control with millions of binary and continuous variables. We demonstrate the potential of this approach to bridge feasible connected components and escape from spurious local minimums in training artificial neural networks. Lastly, in order to solve the resulting convex models, a highly parallelizable numerical method is introduced that can leverage GPUs and distributed computation platforms with orders-of-magnitude time improvements.
Bio: Ramtin Madani is an assistant professor in the Department of Electrical Engineering at University of Texas-Arlington. He earned a Ph.D. degree in electrical engineering from Columbia University in 2015 and was a postdoctoral scholar in the Department of Industrial Engineering and Operations Research at University of California, Berkeley in 2016. His research focuses on developing algorithms for optimization, control and machine learning with real-world applications in energy. Ramtin Madani's work has received the 2016 Best Publication Award in Energy from the Institute for Operations Research and the Management Sciences (INFORMS) Section on Energy, Natural Resources, and the Environment.
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