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

Jointly with Anirudh Subramanyam

Year: 2024

Abstract: We provide a correction to the sufficient conditions under which closed-form expressions for the optimal Lagrange multiplier are provided in arXiv:2112.13138 [math.OC]. 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 the original paper discusses modifications to their method for problems that may not satisfy any sufficient conditions, we substantiate that discussion along two directions. We first show that computing an optimal Lagrange multiplier can still be done in polynomial time. We then provide complete and correct versions of the corresponding Benders and column-and-constraint generation algorithms in which the original method is used. We also discuss the implications of our findings on computational performance.

Cite as:

@techreport{lefebvre2025correctiontolagrangiandual,
  title={Correction to: A Lagrangian dual method for two-stage robust optimization with binary uncertainties},
  author={Henri Lefebvre and Anirudh Subramanyam},
  year={2025},
  archivePrefix={arXiv},
  primaryClass={math.OC},
  url={https://arxiv.org/abs/2411.04307}
}

Open Access

arXiv

Open Data

Instances are available on the GitHub repository of the original paper. AnirudhSubramanyam/RobustOptLagrangianDual.jl

Open Methodology

Nothing to report here.

Open Source

Our code is available on the GitHub repository of the original paper. AnirudhSubramanyam/RobustOptLagrangianDual.jl

Open Educational Resources