Qing Ye
Ph.D. Candidate in Operations Research
H. Milton Stewart School of Industrial and Systems Engineering
Georgia Institute of Technology
Advisor/chairperson:
Dr. Christos Alexopoulos, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Weijun Xie, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Committee members:
Dr. Christos Alexopoulos, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Weijun Xie, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. David Goldsman, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Edwin Romeijn, H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Dr. Grani A. Hanasusanto, Department of Industrial & Enterprise Systems Engineering, University of Illinois Urbana-Champaign
Thesis Title: Theory and Algorithms for Nonconvex Learning and Optimization
Date:
Monday, June 22nd, 2026
Time:
1:00 PM – 2:00 PM EDT
Zoom Link:
https://gatech.zoom.us/j/98113715264
Abstract:
This dissertation contributes to the field of mathematical programming on three fronts by developing: (i) a mixed-integer programming framework for fair classification; (ii) distributionally fair stochastic programming methods based on a Wasserstein fairness measure; and (iii) second-order conic and polyhedral approximations of the exponential cone.
First, we propose a unified mixed-integer optimization framework for fair classification. Unlike surrogate-based approaches, the framework models discrete group fairness measures exactly while jointly optimizing prediction accuracy and regularization. It applies to support vector machines, logistic regression, neural networks, and multiclass models. For support vector machines, we derive an exact mixed-integer conic formulation, establish Fisher consistency, and show that fairness enforcement can be interpreted as unbiased subdata selection. This structure leads to an iterative reselection algorithm with convergence and approximation guarantees. Computational results show that exact fairness modeling yields competitive fairness–accuracy trade-offs and demonstrates the practical scalability of mixed-integer optimization for fair machine learning.
Second, we introduce Distributionally Fair Stochastic Optimization (DFSO), which uses Wasserstein distance to reduce disparities between group utility distributions while allowing a controlled level of inefficiency. We show that the epigraph of the Wasserstein fairness measure admits a mixed-integer convex representation and derive Jensen and Gelbrich lower bounds. We prove tightness properties of the Gelbrich bound and characterize its gap from the Wasserstein fairness measure. These results motivate efficient algorithms whose computational performance is validated on socially relevant stochastic optimization problems.
Finally, we study mixed-integer exponential conic programs arising from models with exponential and logarithmic terms, including logistic regression and entropy optimization. To leverage existing MILP and MISOCP technology, we develop SOC and polyhedral approximation schemes for the exponential cone, establish explicit error and lower-bound guarantees, and implement these approximations within scalable computational frameworks. Numerical experiments show substantial improvements over state-of-the-art exponential cone solvers.