Title: Mixed-integer quadratic optimization with switching constraints
Abstract: Several classes of statistical learning problems can be formulated as mixed-integer nonlinear optimization problems. The continuous variables model statistical parameters to be inferred from data, discrete variables are used to encode logical considerations arising from the choice of these parameters, and the loss functions used are typically nonlinear. In this talk, we study problems where the binary variables are used to model non-convexities associated with the sign of the continuous variables. These problems arise for example in classification problems, where binary variables are used to encode for example 0-1 losses, or problems with fairness constraints, where binary variables are used to count members of the population receiving certain incomes. We develop new approaches for formulations for these classes of problems based on mixed-integer conic optimization technology, resulting in more efficient methods than traditional big-M approaches, and show that the proposed approaches can deliver substantially better solutions than alternatives proposed in the machine learning literature.
Bio: Dr. Andrés Gómez is an Associate Professor in the Department of Industrial and Systems Engineering at the University of Southern California, specializing in discrete and conic optimization with applications in finance, statistics, and machine learning. He earned dual B.S. degrees in Mathematics and Computer Science from Universidad de los Andes (Colombia), followed by an M.S. and Ph.D. in Industrial Engineering and Operations Research from UC Berkeley. Before joining USC in 2019, he served as an Assistant Professor at the University of Pittsburgh. He is the recipient of the Young Investigator Award from the Air Force Office of Scientific Research.
