Mixed-Integer Optimization for Responsible Machine Learning

In the last few decades, Machine Learning (ML) has achieved significant success across domains ranging from healthcare, sustainability, and the social sciences, to criminal justice and finance. But its deployment in increasingly sophisticated, critical, and sensitive areas affecting individuals, the groups they belong to, and society as a whole raises critical concerns around fairness, transparency, … Read more

Solving Decision-Dependent Robust Problems as Bilevel Optimization Problems

Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor exploited computationally. Based on the recent results by Goerigk et al. (2025), this paper is the first one that reformulates a given strictly robust optimization … Read more

Addressing Estimation Errors through Robust Portfolio Optimization

It is well known that the performance of the classical Markowitz model for portfolio optimization is extremely sensitive to estimation errors on the expected asset returns. Robust optimization mitigates this issue. We focus on ellipsoidal uncertainty sets around a point estimate of the expected asset returns. An important issue is the choice of the parameters … Read more

Correction to: A Lagrangian dual method for two-stage robust optimization with binary uncertainties

We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in Subramanyam (2022). We first present a simple counterexample where the original conditions are insufficient, highlight where the original proof fails, and then provide modified conditions along with a correct proof of their validity. Finally, although … Read more

Robust Appointment Scheduling for General Convex Uncertainty Sets

The Appointment Scheduling Problem (ASP) involves scheduling a finite number of customers with uncertain service times, served consecutively by a single server, with the goal of minimizing the weighted costs of waiting time, idle time, and overtime. Previous studies employing stochastic programming were limited to small instances or constrained by restrictive assumptions. We introduce a … Read more

Complexity of the Directed Robust b-matching Problem and its Variants on Different Graph Classes

The b-matching problem is a well-known generalization of the classical matching problem with various applications in operations research and computer science. Given an undirected graph, each vertex v has a capacity b(v), indicating the maximum number of times it can be matched, while edges can also be used multiple times. The problem is solvable in … Read more

Robust combinatorial optimization problems with knapsack constraints under interdiction uncertainty

We present an algorithm for finding near-optimal solutions to robust combinatorial optimization problems with knapsack constraints under interdiction uncertainty. We incorporate a heuristic for generating feasible solutions in a standard row generation approach. Experimental results are presented for set covering, simple plant location, and min-knapsack problems under a discrete-budgeted interdiction uncertainty set introduced in this … Read more

A Toll-Setting Problem with Robust Wardrop Equilibrium Conditions Under Budgeted Uncertainty

We consider the problem of determining optimal tolls in a traffic network in which a toll-setting authority aims to maximize revenues and the users of the network act in the sense of Wardrop’s user equilibrium. The setting is modeled as a mathematical problem with equilibrium constraints and a mixed-integer, nonlinear, and nonconvex reformulation is presented … Read more

A Clustering-based uncertainty set for Robust Optimization

Robust optimization is an approach for handling uncertainty in optimization problems, in which the uncertainty set determines the conservativeness of the solutions. In this paper, we propose a data-driven uncertainty set using a type of volume-based clustering, which we call Minimum-Volume Norm-Based Clustering (MVNBC). MVNBC extends the concept of minimum-volume ellipsoid clustering by allowing clusters … Read more

Heuristic Methods for Γ-Robust Mixed-Integer Linear Bilevel Problems

Due to their nested structure, bilevel problems are intrinsically hard to solve–even if all variables are continuous and all parameters of the problem are exactly known. In this paper, we study mixed-integer linear bilevel problems with lower-level objective uncertainty, which we address using the notion of Γ-robustness. To tackle the Γ-robust counterpart of the bilevel … Read more