Computational Techniques for Nonlinear Optimization and Learning ProblemsThe design of efficient computational techniques for nonlinear optimization has been an active area of research in the field of optimization theory for many years, but has recently been shaping the mathematical foundation of data science. In this walk, we investigate different strategies for finding a high-quality solution of a nonlinear optimization or learning problem. To this end, we develop key notions such as penalized semi-definite programs (SDPs), spurious local trajectory and graphical mutual incoherence and also design algorithms with near-linear time/memory complexity for sparse SDPs with localized constraints to break down the complexity of SDPs and make them as usable as linear programs. Finally, we offer several case studies on real-world systems such as power grids and transportations.
Biography: Javad Lavaei is an Associate Professor in the Department of Industrial Engineering and Operations Research at UC Berkeley. His research spans power systems, optimization theory, control theory, and machine learning. He has won several awards, including DARPA Young Faculty Award, DARPA Director's Fellowship, ONR Young Investigator Award, ONR Director of Research Early Career Grant, AFOSR Young Investigator Award, NSF CAREER Award, Google Faculty Award, and Canadian Governor General's Gold Medal. Javad Lavaei is an associate editor for the IEEE Transactions on Smart Grid, IEEE Transactions on Automatic Control, and IEEE Control Systems Letters. He is a recipient of the 2015 INFORMS Optimization Society Prize for Young Researchers, the 2015 Best Journal Paper Award given by IEEE Power & Energy Society, the 2016 Donald P. Eckman Award given by the American Automatic Control Council, the 2016 INFORMS ENRE Energy Best Publication Award, the 2017 SIAM Control and Systems Theory Prize, and best conference paper finalist awards from the Control Systems Society in 2014, 2019 and 2020. He has also received the Presidential Early Career Award for Scientists and Engineers given by the White House.
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