{
  "abstract": "Several dairy retailers share a refrigerated cold-chain network, each allocating products across heat-sensitivity subgroups to maximize quadratic-fractional efficiency (DEA style). This formulation measures spoilage risk per unit of logistics cost, separating technical from scale efficiency. The single-agent problem is a non-convex fractional QCQP, while the multi-retailer game forms a generalized Nash equilibrium problem (GNEP) with a shared risk-budget constraint, which is generally NP-hard. Governed by the Arrhenius spoilage law, the thermal-risk covariance inherits a rank-one-plus-diagonal structure that unlocks hidden convexity. The authors propose the HSDI (Hidden SOCP Dinkelbach Iteration) algorithm via a joint Cholesky-spectral transform. Key contributions include: 1. Establishing simultaneous diagonalization of without requiring matrix commutativity. 2. Deriving an explicit sufficient condition for exact second-order cone programming (SOCP) relaxation, alongside a closed-form suboptimality bound for inexact regimes. 3. Proving global convergence: the outer Dinkelbach loop converges Q-superlinearly (exact) or R-linearly (inexact), and the coupled variational-equilibrium (VE) iteration converges R-linearly under strong monotonicity, achieving an overall complexity while ensuring Lipschitz stability of the primal-dual pair. Calibrated on Vietnam and US dairy markets, HSDI matches the objective value of multi-start non-linear baselines without random restarts, yielding global optima under exactness. HSDI exhibits an empirical scaling exponent of 0.93 (versus 1.30 for SLSQP), offering a certified polynomial-time framework and a stable shadow price for prioritizing cold-chain investments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36350",
  "author_total": 5,
  "authors": [
    {
      "name": "Thinh Nguyen Hoang Pham"
    },
    {
      "name": "Boris Mordukhovich"
    },
    {
      "name": "Son Hoang Truong"
    },
    {
      "name": "Ngoc Anh Tran"
    },
    {
      "name": "Quyen Phuong Le"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ytn324ted4mw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36350",
  "fulltext_url": null,
  "id": "9ytn324ted4mw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36350",
  "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": "W7224128810",
  "pdf_url": "https://arxiv.org/pdf/2610.36350",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ytn324ted4mw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36350",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36350"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Hidden Convexity in Multi-Retailer Cold-Chain Allocation: A Cholesky-Spectral Second-Order Cone Programming Approach",
  "title_text": "Hidden Convexity in Multi-Retailer Cold-Chain Allocation: A Cholesky-Spectral Second-Order Cone Programming Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/9ytn324ted4mw",
  "venue": "arXiv",
  "versions": []
}