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

Byeon, Geunyeong; Fang, Kaiwen; Kim, Kibaek

doi:10.1137/23m1626839

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

Journal Article · Sat Mar 01 00:00:00 EST 2025 · SIAM Journal on Optimization

DOI:https://doi.org/10.1137/23m1626839· OSTI ID:3000967

^[1]; Fang, Kaiwen ^[1]; ^[2]

Arizona State Univ., Tempe, AZ (United States)
Argonne National Laboratory (ANL), Argonne, IL (United States)

Here, 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 counterexample, 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. Furthermore, cutting-plane-based algorithms, equipped with a unified scenario generation framework, are proposed for addressing both unbounded support and second-stage dual feasible regions, with a finite convergence proof under less stringent assumptions.

View Accepted Manuscript (DOE)

Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 3000967

Journal Information:: SIAM Journal on Optimization, Journal Name: SIAM Journal on Optimization Journal Issue: 1 Vol. 35; ISSN 1095-7189; ISSN 1052-6234

Publisher:: Society for Industrial and Applied Mathematics (SIAM)Copyright Statement

Country of Publication:: United States

Language:: English

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

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