{
  "abstract": "We address the problem of optimally placing a limited number of sensors to reconstruct high-dimensional signals without knowledge of the underlying dynamics. The task is formulated as a nonconvex combinatorial optimisation problem and recast as a weakly convex constrained projection problem. This reformulation allows us to compute $\\varepsilon$-global solutions using the Inexact Cutting Sphere algorithm. We further propose the Inverse Cutting Sphere algorithm, which starts from any feasible heuristic solution and either improves it by a prescribed tolerance $\\varepsilon$ or certifies its $\\varepsilon$-global optimality. The framework is evaluated on pressure reconstruction for NACA airfoils using XFOIL data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.15821",
  "author_total": 1,
  "authors": [
    {
      "name": "Giovanni Bruccola"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/drha8vyvmemzh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.15821",
  "fulltext_url": null,
  "id": "drha8vyvmemzh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.15821",
  "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",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7169798102",
  "pdf_url": "https://arxiv.org/pdf/2607.15821",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/drha8vyvmemzh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2607.15821",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.15821"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Global solutions for the sensors placement problem via weakly convex optimization",
  "title_text": "Global solutions for the sensors placement problem via weakly convex optimization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/drha8vyvmemzh",
  "venue": "arXiv",
  "versions": []
}