{
  "abstract": "We consider constrained problems in which input data are affected by errors. In such settings, Wasserstein distributionally robust optimization provides a principled framework to mitigate model risk by optimizing against worst-case data distributions within Wasserstein ambiguity sets. However, the numerical resolution of the resulting problems remains challenging, especially in constrained settings. In this paper, we provide a general, practical way to solve Wasserstein distributionally robust formulations in the presence of constraints. Our approach only requires a linear minimization oracle for the feasible set, and combines two key ingredients: (i) an entropic regularization of the distributionally robust value function, which makes it possible to compute stochastic gradient estimators, and (ii) a stochastic Frank-Wolfe algorithm, which minimizes the regularized robust objective while naturally handling constraints. We illustrate the method, its tractability, and its interests against empirical risk minimization, on two problems: the traffic assignment and the minimum quadratic spanning tree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.11460",
  "author_total": 3,
  "authors": [
    {
      "name": "Hubert Villuendas"
    },
    {
      "name": "Mathieu Besançon"
    },
    {
      "name": "Jérôme Malick"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fjqd007xz21he.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.11460",
  "fulltext_url": null,
  "id": "fjqd007xz21he",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.11460",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Risk and Portfolio Optimization"
    ]
  ],
  "openalex": "W7168283162",
  "pdf_url": "https://arxiv.org/pdf/2607.11460",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fjqd007xz21he.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2607.11460",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.11460"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "First-Order Methods for Wasserstein Distributionally Robust Constrained Optimization",
  "title_text": "First-Order Methods for Wasserstein Distributionally Robust Constrained Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/fjqd007xz21he",
  "venue": "arXiv",
  "versions": []
}