{
  "abstract": "We propose an algorithmic framework for solving adaptive robust optimization with provable guarantees on both tractability and solution accuracy. The framework introduces soft separation, a probabilistic mechanism for identifying worst-case uncertainty realizations via a time-inhomogeneous Markov chain. Rather than solving an exact separation problem in each iteration, which is intractable in general, the chain carries adversarial information across iterations, co-evolves with the optimization iterates, and recovers exact separation at terminal iterates with high probability. For continuous first-stage (here-and-now) decisions, we design a first-order method that uses soft separation to produce adaptive gradient estimates. Notably, we prove polynomial-time convergence in expectation to the global optimum. For mixed-integer here-and-now decisions, we embed soft separation within a branch-and-cut framework to generate valid cuts for the robust objective and obtain a high-probability certificate of global optimality. Numerical experiments demonstrate that the proposed methods scale favorably with problem dimension and scenario size relative to state-of-the-art approaches. The instances and code are available online at https://github.com/xuqy2002/SoftSeparationARO.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36275",
  "author_total": 2,
  "authors": [
    {
      "name": "Qingyuan Xu"
    },
    {
      "name": "Ruiwei Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cvpf6srq5tqfm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36275",
  "fulltext_url": null,
  "id": "cvpf6srq5tqfm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36275",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1803|Risk and Portfolio Optimization"
    ]
  ],
  "openalex": "W7214984092",
  "pdf_url": "https://arxiv.org/pdf/2609.36275",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cvpf6srq5tqfm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.36275",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36275"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Soft Separation for Adaptive Robust Optimization",
  "title_text": "Soft Separation for Adaptive Robust Optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/cvpf6srq5tqfm",
  "venue": "arXiv",
  "versions": []
}