Electrical Engineering Seminar
Friday, November 8
11:00am - 12:00pm
SEC LL2.221

"Practical algorithms for sums-of-squares optimization"
Dávid Papp, North Carolina State University


Polynomial optimization problems are very general (and therefore challenging) non-convex minimization problems with algebraic structure that allows the computation of rigorously certifiable global lower bounds that (under broad conditions) can be arbitrarily close to the global minimum. The most common approach for computing these lower bounds uses sums-of-squares relaxations and semidefinite programming. After a general introduction to this area and its most frequently used numerical methods, the talk will focus on the two main computational challenges: the impractical computational complexity and the terrible numerical conditioning of the resulting semidefinite programs. We will investigate how both can be mitigated by using polynomial interpolation and replacing all-purpose semidefinite programming algorithms with either more specialized ones or with non-symmetric cone programming methods that can optimize directly over sums-of-squares cones.

Bio: Dr. Dávid Papp is an associate professor in the Department of Mathematics at NC State. After studying at the Budapest University of Technology and Economics in Hungary, he obtained his PhD in operations research at Rutgers University in 2011. Before joining NC State, he worked at Northwestern University and at the Massachusetts General Hospital. His research focuses on the design, analysis, and implementation of algorithms for solving large-scale optimization problems and their applications in healthcare, engineering, and statistics. His radiotherapy optimization algorithms were built into two clinical treatment planning software used worldwide (Philips Pinnacle and RaySearch RayStation). He received the Mehrotra Award from the INFORMS Health Applications Society in 2021 for his work on radiation therapy and the NSF CAREER Award in 2019 for his research in computational mathematics.