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Robust optimization
Distributional robust optimization
Robust integer optimization
Robust combinatorial optimization
Robust machine and deep learning
Robust control problems
Organizers: Ahmadreza Marandi (TU Eindhoven) and Jannis Kurtz (University of Amsterdam)
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Applying robust optimization often requires selecting an appropriate uncertainty set both in shape and size, a choice that directly affects the trade-off between average-case and worst-case performances. In practice, this calibration is usually done via trial-and-error: solving the robust optimization problem many times with different uncertainty set shapes and sizes, and examining their performance trade-off. In this work, we take a principled approach to study this problem for robust optimization problems with linear objective functions, convex feasible regions, and convex uncertainty sets. We introduce and study what we define as the robust path: a set of robust solutions obtained by varying the uncertainty set's radius. Our central geometric insight is that a robust path can be characterized as a Bregman projection of a curve (whose geometry is defined by the uncertainty set) onto the feasible region. This leads to a surprising discovery that the robust path can be approximated via the trajectories of a related optimization algorithm, such as a tailored proximal point method, of the deterministic counterpart problem. We give a sharp approximation error bound and show it depends on the geometry of the feasible region and the uncertainty set. We also illustrate two special cases where the approximation error is zero: the feasible region is polyhedrally monotone (e.g., a simplex feasible region under an ellipsoidal uncertainty set), or the feasible region and the uncertainty set follow a dual relationship. We show numerical experiments in two settings: portfolio optimization and adversarial deep learning.
Manuscript: https://arxiv.org/abs/2508.20039
Peter Zhang is an Assistant Professor at Carnegie Mellon University’s Heinz College of Information Systems and Public Policy, with a courtesy appointment in engineering.
He earned his PhD in Engineering Systems from MIT and specializes in optimization, robust decision-making, and data-driven analytics for supply chains and transportation.
His research, published in Operations Research, Mathematical Programming, Transportation Research, focuses on resilience, fairness, and predictive modeling in large-scale systems — challenges central to designing resilient supply chains.
He has been recognized with the INFORMS Junior Faculty Paper Competition 1st Place, Koopman Prize, the Wagner Prize, and other awards for advancing both theory and practice-relevant optimization.