Seminar Series | Convexification for Non-Convex Mixed-Integer Quadratic Programming

Speaker: Sam Burer, University of Iowa

Title: Convexification for Non-Convex Mixed-Integer Quadratic Programming

Abstract: Convexification is an important technique used for solving non-convex mixed-integer quadratic programs. We discuss two recent convexification results for nonconvex quadratic programming over: (i) continuous (x1,x2) and binary (y1,y2) such that (0,0) <= (x1,x2) <= (y1,y2); and (ii) the intersection of several Euclidean balls. Although these structures may seem quite specialized, they appear as critical substructures in numerous applications. In addition to describing these two results, we survey the landscape---and the current research frontier---of convexification techniques in this area.

Bio: Sam Burer is the Tippie Rollins Professor in the Department of Business Analytics at the University of Iowa. He received his Ph.D. from Georgia Tech, and his research focuses on convex optimization. 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.