arXiv subjects

Johannes Thürauf

Publications and source records attributed to Johannes Thürauf.

6 recordsLinked to original sources

arXiv2026

A Computational Study for 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 provides an extensive computational study for solving strictly robust optimization problems with decision-dependent uncertainty sets as equivalent bilevel optimization problems. If the uncertainty set can be dualized, the respective bilevel techniques to obtain a single-level reformulation are very similar compared with the classic dualization techniques used in robust optimization but lead to larger single-level problems to be solved. Our numerical study shows that this usually leads to larger computation times. For the more challenging case of decision-dependent uncertainty sets represented by mixed-integer linear models, one cannot apply classic dualization techniques from robust optimization. Thus, we compare the presented bilevel approach with an established method from the literature, which is based on quantified mixed-integer linear programs. Our numerical results indicate that, for the problem class of decision-dependent robust optimization problems with mixed-integer linear uncertainty sets, the bilevel approach performs better in terms of computation times.

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arXiv2026

On Coupling Constraints in Pessimistic Linear Bilevel Optimization

The literature on pessimistic linear bilevel optimization with coupling constraints is rather scarce and it has been common sense that these problems are harder to tackle than pessimistic bilevel problems without coupling constraints. In this note, we show that this is not the case. To this end, given a pessimistic problem with coupling constraints, we derive a pessimistic problem without coupling constraints that has the same set of globally optimal solutions. Moreover, our results also show that one can equivalently replace a pessimistic problem with such constraints with an optimistic problem without coupling constraints. This paves the way of both transferring theory and solution techniques from any type of these problems to any other one.

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arXiv2025

Instance-Optimized String Fingerprints

Recent research found that cloud data warehouses are text-heavy. However, their capabilities for efficiently processing string columns remain limited, relying primarily on techniques like dictionary encoding and prefix-based partition pruning. In recent work, we introduced string fingerprints - a lightweight secondary index structure designed to approximate LIKE predicates, albeit with false positives. This approach is particularly compelling for columnar query engines, where fingerprints can help reduce both compute and I/O overhead. We show that string fingerprints can be optimized for specific workloads using mixed-integer optimization, and that they can generalize to unseen table predicates. On an IMDb column evaluated in DuckDB v1.3, this yields table-scan speedups of up to 1.36$\times$.

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arXiv2025

Adjustable Robust Nonlinear Network Design Without Controllable Elements under Load Scenario Uncertainties

We study network design problems for nonlinear and nonconvex flow models without controllable elements under load scenario uncertainties, i.e., under uncertain injections and withdrawals. To this end, we apply the concept of adjustable robust optimization to compute a network design that admits a feasible transport for all, possibly infinitely many, load scenarios within a given uncertainty set. For solving the corresponding adjustable robust mixed-integer nonlinear optimization problem, we show that a given network design is robust feasible, i.e., it admits a feasible transport for all load scenario uncertainties, if and only if a finite number of worst-case load scenarios can be routed through the network. We compute these worst-case scenarios by solving polynomially many nonlinear optimization problems. Embedding this result for robust feasibility in an adversarial approach leads to an exact algorithm that computes an optimal robust network design in a finite number of iterations. Since all of the results are valid for general potential-based flows, the approach can be applied to different utility networks such as gas, hydrogen, or water networks. We finally demonstrate the applicability of the method by computing robust gas networks that are protected from future load fluctuations.

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arXiv2024

On Coupling Constraints in Linear Bilevel Optimization

It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and without coupling constraints w.r.t. their complexity-theoretical hardness. In this note, we prove that, although there is a clear difference between these two classes of problems in terms of their feasible sets, the classes are equivalent on the level of optimal solutions. To this end, given a general linear bilevel problem with coupling constraints, we derive a respective problem without coupling constraints and prove that it has the same optimal solutions (when projected back to the original variable space).

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arXiv2023

On a Computationally Ill-Behaved Bilevel Problem with a Continuous and Nonconvex Lower Level

It is well known that bilevel optimization problems are hard to solve both in theory and practice. In this paper, we highlight a further computational difficulty when it comes to solving bilevel problems with continuous but nonconvex lower levels. Even if the lower-level problem is solved to $\varepsilon$-feasibility regarding its nonlinear constraints for an arbitrarily small but positive $\varepsilon$, the obtained bilevel solution as well as its objective value may be arbitrarily far away from the actual bilevel solution and its actual objective value. This result even holds for bilevel problems for which the nonconvex lower level is uniquely solvable, for which the strict complementarity condition holds, for which the feasible set is convex, and for which Slater's constraint qualification is satisfied for all feasible upper-level decisions. Since the consideration of $\varepsilon$-feasibility cannot be avoided when solving nonconvex problems to global optimality, our result shows that computational bilevel optimization with continuous and nonconvex lower levels needs to be done with great care. Finally, we illustrate that the nonlinearities in the lower level are the key reason for the observed bad behavior by showing that linear bilevel problems behave much better at least on the level of feasible solutions.

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