Season 7 

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.

Robust optimization (RO) and distributionally robust optimization (DRO), as relatively new optimization schemes, have been adopted in many practical systems (e.g., power, logistics and healthcare systems) to support their design, operations, and reliabilities. Especially, due to the sophisticated and nested min-max structure, two-stage DRO is often studied using duality-based techniques, aiming to simplify its structure and obtain monolithic reformulations. Nevertheless, research developed from such dual perspective is rather abstract and technically demanding, which is less friendly to build intuitive understanding or for further development.

In this talk, unlike existing research, we take the primal perspective to analyze RO and DRO, and directly make use of their primal structures to develop computational algorithms. The resulting algorithm and its variants are, overall, simple, intuitive, and application-friendly. A couple of unsolved issues are also investigated under this solution framework. In particular, we show how this framework can be extended by leveraging AI, specifically generative adversarial networks (GANs), and parallel computing to achieve significant performance improvements. Through illustrative examples in logistics, production, and energy systems, along with computational results, we demonstrate how these methods can be effectively applied in practice.

Dr. Zeng is an Associate Professor of Industrial Engineering in the Swanson School of Engineering at the University of Pittsburgh where he teaches and conducts research on discrete and robust optimization, with applications in logistics, energy, and healthcare systems. Prior to that, he worked as an assistant professor of Industrial and Management Systems Engineering at the University of South Florida. Through his research, Dr. Zeng has developed several analytical operational models and algorithms (e.g., the basic column-and-constraint generation method and its variants) that have been extensively applied in energy, logistics and other critical infrastructure systems, to address real design and operational issues and to hedge against risks and to achieve better reliability and security.  He is a professional member of IISE, INFORMS and IEEE. 

We study learning in an adversarial setting, where an epsilon fraction of samples from a distribution P are globally corrupted (arbitrarily modified), and the remaining perturbations have an average magnitude bounded by rho (local corruptions). With access to n such corrupted samples, we aim to develop a computationally efficient approach that achieves the optimal minimax excess risk. Our approach combines a data-driven cleaning module with a distributionally robust optimization (DRO) framework. We demonstrate that if the data cleaning module is minimax optimal with respect to the Wasserstein loss, solving an optimal transport-based DRO problem ensures a minimax optimal decision. We further provide tractable reformulations for both modules. Specifically, we introduce an optimal filtering algorithm to clean corrupted data by identifying and removing outliers. For the DRO module, we reformulate the problem as a two-player zero-sum game, deriving finite convex formulations. We show that the minimax theorem applies to this game, and Nash equilibria exist. Finally, we present a principled approach for constructing adversarial examples.

Soroosh Shafiee is an assistant professor in the School of Operations Research and Information Engineering at Cornell University. Before that, he held positions as a postdoctoral researcher at both the Tepper School of Business at Carnegie Mellon University and the Automatic Control Laboratory at ETH Zurich. He held a B.Sc. and M.Sc. degree in Electrical Engineering from the University of Tehran and a Ph.D. degree in Management of Technology from EPFL. His primary research interests revolve around low-complexity decision-making, optimization under uncertainty and optimal transport. He is a recipient of the NSF CAREER Award and the SNF Postdoc.Mobility Fellowship.

Counterfactual analysis is a powerful tool in explainable machine learning. Given a prediction model and an input record, one seeks a minimal perturbation (with respect to a prescribed metric) of the record such that the prediction for the perturbed instance attains a specified threshold value. This can be formulated as a mathematical optimization problem, whose structural properties depend on the prediction model and the feature space. It is typically assumed that the feature values are unaffected by measurement or aggregation errors, that the counterfactual intervention can be implemented exactly, and that the prediction coincides with the ground-truth value of the response variable. When these assumptions fail, robustness considerations become essential to ensure that the resulting counterfactual explanation is reliable. In this talk, I will review recent research on this topic developed jointly with Renato de Leone (University of Camerino), Marica Magagnini (University of Camerino), and Antonio Navas-Orozco (University of Seville). The focus will be on the corresponding optimization problems and on the approaches proposed to (heuristically) solve them.

Emilio is Full Professor of Statistics and Operations Research at the University of Seville. His research focuses on Mathematical Optimization, Operations Research, and Data Science, with applications in industrial and applied mathematics. He is President of math-in, the Spanish Network for Industrial Mathematics, and has previously served as Director of IMUS, the Institute of Mathematics of the University of Seville, and President of SEIO, the Spanish Society of Statistics, Operations Research and Data Science. He also served as Editor-in-Chief of TOP, the Society’s journal in Operations Research. He is the author of more than 150 publications, including articles in leading journals such as Operations Research, Mathematical Programming, Management Science, and Mathematics of Operations Research. He is actively engaged in knowledge transfer and industrial collaborations across the energy, health, logistics, and technology sectors.

In this talk, we present new perspectives on distributionally robust optimization (DRO) by considering multimodal ambiguity sets and decision-dependent uncertainties with models, solution algorithms, and applications. We first provide a two-stage DRO model with multimodal uncertainty, where both the mode probabilities and uncertainty distributions could be affected by the first-stage decisions. To address this setting, we propose a generic framework by introducing a phi-divergence based ambiguity set to characterize the decision-dependent mode probabilities and consider both moment-based and Wasserstein distance-based ambiguity sets to characterize the uncertainty distribution under each mode. We identify two special phi-divergence examples (variation distance and χ2-distance) and provide specific forms of decision dependence relationships under which we can derive tractable reformulations. Furthermore, we investigate the benefits of considering multimodality in a DRO model compared to a single-modal counterpart through an analytical analysis. Additionally, we develop a separation-based decomposition algorithm to solve the resulting DRO models with finite convergence and optimality guarantee under certain settings. We provide a detailed computational study over two example problem settings, facility location problem and shipment planning problem with pricing, to illustrate our results, which demonstrate that omission of multimodality or decision-dependent uncertainties within DRO frameworks result in inadequately performing solutions with worse in-sample and out-of-sample performances under various settings. We further demonstrate the speed-ups obtained by the solution algorithm against the off-the-shelf solver over various instances. Additionally, we present another application of DRO under decision-dependent uncertainty through a capacity expansion planning problem considering the chicken-and-egg dilemma under uncertain market conditions. We derive tractable reformulations of this problem under certain settings and develop a tailored algorithm based on the column-and-constraint generation approach providing computationally efficient solution approaches. 

Beste Basciftci is an Assistant Professor at the Department of Business Analytics at the Tippie College of Business at the University of Iowa. She is broadly interested in data-driven decision-making problems under uncertainty by developing mixed-integer/discrete optimization, stochastic programming, and distributionally robust optimization approaches to address methodological and computational challenges arising in operations research and management related problems. Main application areas of her research include energy systems and sustainability, supply chains and facility location problems, and emerging transportation and sharing systems. She obtained her PhD in operations research from the H. Milton Stewart School of Industrial and Systems Engineering at Georgia Institute of Technology and obtained bachelor's degrees in industrial engineering and computer engineering (double major) from Bogazici University with High Honors. She has received various recognitions for her research including INFORMS ENRE (Energy, Natural Resources and the Environment Section) Early Career Best Paper Award Runner-up, IISE Transactions Best Paper Award in Focus Issue of Operations Engineering & Analytics, Tippie College of Business Social Impact Research Award, University of Iowa Early Career Scholar Award, and Georgia Tech ISyE Alice and John Jarvis Research Award. Her research is supported by the National Science Foundation and is honored to be elected to the Board of the INFORMS Computing Society and to the Committee on Stochastic Programming of the Mathematical Optimization Society.

We consider a fundamental generalization of the classical newsvendor problem where the seller needs to decide on the inventory of a product jointly for multiple locations on a metric as well as a fulfillment policy to satisfy the uncertain demand that arises sequentially over time after the inventory decisions have been made. To address the distributional-ambiguity, we consider a distributionally robust setting where the decision-maker only knows the mean and variance of the demand, and the goal is to make inventory and fulfillment decisions to minimize the worst-case expected inventory and fulfillment cost (where the expectation is taken over the worst case choice of distribution with given mean and variance).  

We present a significant generalization of the classical result of Scarf (1958) and give a policy with strong theoretical guarantees as well as good practical performance while maintaining the simplicity and interpretability of the solution in Scarf (1958). In particular, our policy first identifies a hierarchical clustering of the locations, and assigns a "virtual-underage cost" for each cluster. Our inventory solution ensures that for each cluster, the total inventory in the cluster is at least as large as the inventory level suggested by Scarf's solution for the virtual-underage cost if the cluster was a single point. We present a worst-case performance guarantee for our policy and also demonstrate that the policy performs well in practice. To the best of our knowledge, this is the first algorithm with provable performance guarantees.  

(This is joint work with Ayoub Foussoul)

Vineet Goyal is Professor in the Industrial Engineering and Operations Research Department at Columbia University where he joined in 2010 after his PhD in Algorithms, Combinatorics, and Optimization (ACO) from Carnegie Mellon University in 2008 and Postdoc at the Operations Research Center at MIT. He is interested in the design of efficient and robust data-driven algorithms for large scale dynamic optimization problems with applications in revenue management, health care and resource allocation problems. His research has been continually supported by grants from NSF, DARPA and industry including NSF CAREER Award in 2014 and faculty research awards from Google, IBM, Adobe, and Amazon.