{
  "abstract": "This paper proposes a new robust optimization (RO) formulation namely the RO under objective functional uncertainty (ObRO). The ObRO adopts a min-max structure where the inner problem finds the worst-case objective function in a continuous function space to maximize the cost, and the outer problem finds the optimal decision in a Euclidean space to minimize the cost. A solution algorithm is designed to alternately generate the worst-case objective function at the current decision and the optimal decision for the current collection of objective functions. Using operator theory, we prove that this algorithm converges to the defined ``semi-global'' saddle point of the ObRO problem. In addition, we propose a numerical solver based on the piece-wise linearization (PWL) approximation of objective functions. The PWL approximate problem is proved to be numerically consistent with the original ObRO problem. The obtained results are applied to the degradation-aware battery charging scheduling in distribution networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: IEEE Transactions on Automatic Control, 2027",
  "arxiv": "2605.18669",
  "author_total": 5,
  "authors": [
    {
      "name": "Yue Song"
    },
    {
      "name": "Yuxi Lu"
    },
    {
      "name": "Gang Li"
    },
    {
      "name": "Kairui Feng"
    },
    {
      "name": "Qi Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8azw1et720yw9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.18669",
  "fulltext_url": null,
  "id": "8azw1et720yw9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.18669",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.18669",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8azw1et720yw9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2605.18669",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.18669"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Robust Optimization Under Objective Functional Uncertainty",
  "title_text": "Robust Optimization Under Objective Functional Uncertainty",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/8azw1et720yw9",
  "venue": "arXiv",
  "versions": []
}