single-level reformulation – Optimization Online

A true single–level reformulation for pessimistic bilevel optimization

Published: 2026/08/01, Updated: 2026/09/29

We propose a single-level reformulation (SLR) for the pessimistic bilevel optimization problem that does not rely on complementarity conditions or optimal value functions. For this reason, we refer to it as a true single-level reformulation (tSLR). A remarkable consequence is that this reformulation can satisfy the classical linear independence constraint qualification, despite the fact that … Read more

Robust Optimization Under Controllable Uncertainty

Published: 2023/09/04, Updated: 2025/07/02

Combinatorial Optimization, Robust Optimization budgeted uncertainty, controllable uncertainty, explorable uncertainty, mixed-integer programming, multi-level optimization, robust optimization, single-level reformulation

Applications for optimization with uncertain data in practice often feature a possibility to reduce the uncertainty at a given query cost, e.g., by conducting measurements, surveys, or paying a third party in advance to limit the deviations. To model this type of applications we introduce the concept of optimization problems under controllable uncertainty (OCU). For … Read more