Abstract: In this talk, Prof. Freund will present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. He will present computational guarantees for the method that trade off efficiency in computing near-optimal solutions with upper bounds on the dimension of minimal faces of iterates. Prof. Freund will apply this method to the low-rank matrix completion problem, where low-dimensional faces correspond to low-rank solutions. He’ll also present computational results for large-scale low-rank matrix completion problems that demonstrate significant speed-ups in computing low-rank near-optimal solutions on both artificial and real datasets. This is joint work with Paul Grigas (ORC) and Rahul Mazumder (Sloan).
Bio: Robert Freund is the Theresa Seley Professor in Management Science at the Sloan School of Management at MIT. His current research interests are in convex optimization and algorithms for huge-scale problems in data science. He has served as co-editor of the journal Mathematical Programming and as associate editor of several optimization and operations research journals. He is the former co-director of MIT Operations Research Center and the MIT Program in Computation for Design and Optimization, and has served as former chair of the INFORMS Optimization Section.
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