10/9/25 | 4:15pm | E51-145
Andres Gomez
Associate Professor, Department of Industrial and Systems Engineering
University of Southern California
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 is typically nonlinear. In this talk, we study problem 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 optimization and machine learning. His research develops advanced mixed-integer and nonlinear optimization methodologies with applications in responsible AI, finance, and large-scale decision-making. Gómez has introduced novel convexification techniques for challenging nonconvex problems, advancing the training of interpretable, fair, and robust machine learning models. His work has been recognized with multiple research grants from NSF, AFOSR, ONR Google, Meta, and Capital One, including a Young Investigator Program award.