{
  "id": "2402.12090",
  "version": "v1",
  "published": "2024-02-19T12:12:32.000Z",
  "updated": "2024-02-19T12:12:32.000Z",
  "title": "Characterization of optimization problems that are solvable iteratively with linear convergence",
  "authors": [
    "Foivos Alimisis"
  ],
  "categories": [
    "math.OC",
    "math.DG"
  ],
  "abstract": "In this work, we state a general conjecture on the solvability of optimization problems via algorithms with linear convergence guarantees. We make a first step towards examining its correctness by fully characterizing the problems that are solvable via Riemannian gradient descent with linear convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-19T12:12:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "optimization problems",
      "characterization",
      "linear convergence guarantees",
      "riemannian gradient descent",
      "first step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}