Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls

Geunyeong Byeon; Kaiwen Fang; Kibaek Kim

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arXiv · 2211.05903

Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls

Geunyeong Byeon·Kaiwen Fang·Kibaek Kim

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Abstract

This paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 Wasserstein balls. We present optimality conditions for the dual of the worst-case expectation problem, which characterizes worst-case uncertain parameters for its inner maximization problem. This condition offers an alternative proof, a counter-example, and an extension to previous works. Additionally, the condition highlights the potential advantage of a specific distance metric for out-of-sample performance, as exemplified in a numerical study on a facility location problem with demand uncertainty. A cutting-plane-based algorithm and a variety of algorithmic enhancements are proposed with a finite convergence proof under less stringent assumptions.

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BibTeX RIS

Geunyeong Byeon, Kaiwen Fang, Kibaek Kim. 2022-11-10. Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls. https://arxiv.org/abs/2211.05903

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