UTRC CDS Invited Lecture: Javad Lavaei "Graph-Theoretic Convexification of Polynomial Optimization"
Friday, November 18, 2016
2168 A V Williams
301 405 6576
UTRC Control and Dynamical Systems Invited Lecture Series
Graph-Theoretic Convexification of Polynomial Optimization Problems with Applications to Power Systems and Distributed Control
Department of Industrial Engineering and Operations Research
University of California, Berkeley
The area of polynomial optimization has been actively studied in computer science, operations research, applied mathematics and engineering, where the goal is to find a high-quality solution using an efficient computational method. This area has attracted much attention in the control community since several long-standing control problems could be converted to polynomial optimization problems. The current researches on this area have been mostly focused on various important questions: i) how does the underlying structure of an optimization problem affect its complexity? Ii) how does sparsity help? iii) how to find a near globally optimal solution whenever it is hard to find a global minimum? iv) how to design an efficient numerical algorithm for large-scale non-convex optimization problems? v) how to deal with problems with a mix of continuous and discrete variables? In this talk, we will develop a unified mathematical framework to study the above problems. Our framework rests on recent advances in graph theory and optimization, including the notions of OS-vertex sequence and treewidth, matrix completion, semidefinite programming, and low-rank optimization. We will also apply our results to two areas of power systems and distributed control. In particular, we will discuss how our results could be used to address several hard problems for power systems such as optimal power flow (OPF), security-constrained OPF, state estimation, and unit commitment.
Javad Lavaei is an Assistant Professor in the Department of Industrial Engineering and Operations Research at University of California, Berkeley. He was an Assistant Professor in Electrical Engineering at Columbia University from 2012 to 2015. He received the Ph.D. degree in Control & Dynamical Systems from the California Institute of Technology in 2011, and was a postdoctoral scholar in Electrical Engineering and Precourt Institute for Energy at Stanford University for one year. He is the recipient of the Milton and Francis Clauser Doctoral Prize for the best university-wide Ph.D. thesis, entitled "Large-Scale Complex Systems: From Antenna Circuits to Power Grids". He researches on optimization theory, control theory and power systems. He has won several awards, including DARPA Young Faculty Award, Office of Naval Research Young Investigator Award, National Science Foundation CAREER Award, Resonate Award, Google Faculty Research Award, Governor General of Canada Academic Gold Medal, Northeastern Association of Graduate Schools Master's Thesis Award, and Silver Medal in the 1999 International Mathematical Olympiad. Javad Lavaei is an associate editor of IEEE Transactions on Smart Grid and serves on the conference editorial board of IEEE Control Systems Society and European Control Association. He was a finalist (as an advisor) for the Best Student Paper Award at the 53rd IEEE Conference on Decision and Control 2014. His journal paper entitled "Zero Duality Gap in Optimal Power Flow Problem" has received a prize paper award given by the IEEE PES Power System Analysis Computing and Economics Committee in 2015. He is a co-recipient of the 2015 INFORMS Optimization Society Prize for Young Researchers, and the recipient of the 2016 Donald P. Eckman Award given by the American Automatic Control Council.