{
  "annotation_id": "75899517-6b3a-4f7b-bed6-a23ace2c3f53",
  "date_created": "2026-02-17T05:53:08.234000Z",
  "date_modified": "2026-02-17T05:53:08.234000Z",
  "file_hash": "d2931abcd5b78dd6ef146a78b35293b6cd0c0e8157416de3ad8b3d3e94b4dbec",
  "private": false,
  "record": {
    "abstract": "We introduce $\\textsf{gradOL}$, the first gradient-based optimization framework for solving Chebyshev center problems, a fundamental challenge in optimal function learning and geometric optimization. $\\textsf{gradOL}$ hinges on reformulating the semi-infinite problem as a finitary max-min optimization, making it amenable to gradient-based techniques. By leveraging automatic differentiation for precise numerical gradient computation, $\\textsf{gradOL}$ ensures numerical stability and scalability, making it suitable for large-scale settings. Under strong convexity of the ambient norm, $\\textsf{gradOL}$ provably recovers optimal Chebyshev centers while directly computing the associated radius. This addresses a key bottleneck in constructing stable optimal interpolants. Empirically, $\\textsf{gradOL}$ achieves significant improvements in accuracy and efficiency on 34 benchmark Chebyshev center problems from a benchmark $\\textsf{CSIP}$ library. Moreover, we extend $\\textsf{gradOL}$ to general convex semi-infinite programming (CSIP), attaining up to $4000\\times$ speedups over the state-of-the-art $\\texttt{SIPAMPL}$ solver tested on the indicated $\\textsf{CSIP}$ library containing 67 benchmark problems. Furthermore, we provide the first theoretical foundation for applying gradient-based methods to Chebyshev center problems, bridging rigorous analysis with practical algorithms. $\\textsf{gradOL}$ thus offers a unified solution framework for Chebyshev centers and broader CSIPs.",
    "arxiv_id": "2601.06434",
    "authors": [
      "Abhinav Raghuvanshi",
      "Mayank Baranwal",
      "Debasish Chatterjee"
    ],
    "categories": [
      "math.OC",
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On a Gradient Approach to Chebyshev Center Problems with Applications to Function Learning",
    "url": "https://arxiv.org/abs/2601.06434",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a62bf4e1-1f91-45cd-8ef7-3765ac935d10",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}