{
  "id": "2311.09723",
  "version": "v1",
  "published": "2023-11-16T09:55:57.000Z",
  "updated": "2023-11-16T09:55:57.000Z",
  "title": "A study of Geodesic (E, F)-preinvex Functions on Riemannian Manifolds",
  "authors": [
    "Ehtesham Akhter",
    "Musavvir Ali"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "In this manuscript, we define (E, F)-invex set, (E, F)-invex functions, and (E, F)-preinvex functions on Euclidean space. We explore the concepts on the Riemannian manifold. We also detail the fundamental properties of (E, F)-preinvex functions and some examples that illustrate the concepts well. We have established a relation between (E, F)-invex and (E, F)-preinvex functions on the Riemannian manifolds. We introduce the conditions A and define (E, F)-proximal sub-gradient. To explore and demonstrate its applicability to optimization problems, (E, F)-preinvex is utilized. In the last, we establish the points of extrema of a non-smooth (E, F)-preinvex functions on (E, F)-invex subset of the Riemannian manifolds by using (E, F)-proximal sub-gradient.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-16T09:55:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemannian manifold",
      "euclidean space",
      "fundamental properties",
      "sub-gradient",
      "optimization problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}