Thought Leaders Seminar, Business Analytics: Sam Burer

Apr 7, 2023

01:00 PM - 02:00 PM

Pappajohn Business Building, C125

21 East Market Street, Iowa City, IA 52245

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Topic: Two Decades of Low-Rank Optimization

Big data matrices are often low rank, and so modern optimization algorithms often require the use of low-rank decision variables. Such variables also arise naturally in certain optimization problems, irrespective of the input data. As a result, over the past two decades, low-rank optimization has grown as a critical area of research in optimization and machine learning. However, enforcing low-rank structure on a variable gives rise to severe nonconvexities, challenging the design of high-quality algorithms. In this talk, we offer our personal perspective on low-rank algorithms for semidefinite programs and related matrix optimization problems. We touch on their history and describe connections with other trends in optimization, including first-order methods and benign nonconvexity. Finally, we highlight recent theoretical insights into low-rank algorithms—as well as various applications for which low-rank approaches have proven successful.

Sam Burer is the Tippie Rollins Professor in the Department of Business Analytics at the University of Iowa. He received his PhD from the Georgia Institute of Technology, and his research focuses on convex optimization, especially semidefinite and copositive programming. He is the recipient of the 2020 INFORMS Computing Paper Prize and the 2023 SIAM Optimization Test of Time Award. His work has been supported by grants from the National Science Foundation, including the CAREER award, and he currently serves as an area editor of Operations Research and as an associate editor for SIAM Journal on Optimization and Mathematical Programming. He also serves as Treasurer of the Mathematical Optimization Society and is a past Vice Chair of the SIAM Activity Group on Optimization.

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