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
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
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
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
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
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
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
Robust Optimization (RO) is an approach to tackle uncertainties in the parameters of an optimization problem. Constructing an uncertainty set is crucial for RO, as it determines the quality and the conservativeness of the solutions. In this paper, we introduce an approach for constructing a data-driven uncertainty set through volume-based clustering, which we call Minimum-Volume … Read more
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
Robust optimization (RO) is a powerful paradigm for decision making under uncertainty. Existing algorithms for solving RO, including the reformulation approach and the cutting-plane method, do not scale well, hindering the application of RO to large-scale decision problems. In this paper, we devise a first-order algorithm for solving RO based on a novel max-min-max perspective. … Read more