{
  "id": "2401.13316",
  "version": "v1",
  "published": "2024-01-24T09:16:05.000Z",
  "updated": "2024-01-24T09:16:05.000Z",
  "title": "On the supporting quasi-hyperplane and separation theorem of geodesic convex sets with applications on Riemannian manifolds",
  "authors": [
    "Li-wen Zhou",
    "Ling-ling Liu",
    "Chao Min",
    "Yao-jia Zhang",
    "Nan-Jing Huang"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this paper, we first establish the separation theorem between a point and a locally geodesic convex set and then prove the existence of a supporting quasi-hyperplane at any point on the boundary of the closed locally geodesic convex set on a Riemannian manifold. As applications, some optimality conditions are obtained for optimization problems with constraints on Riemannian manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-24T09:16:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian manifold",
      "separation theorem",
      "supporting quasi-hyperplane",
      "applications",
      "closed locally geodesic convex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}