{
  "id": "2209.02177",
  "version": "v1",
  "published": "2022-09-06T02:00:44.000Z",
  "updated": "2022-09-06T02:00:44.000Z",
  "title": "Duality for Composite Optimization Problem within the Framework of Abstract Convexity",
  "authors": [
    "The Hung Tran",
    "Ewa Bednarczuk"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "We study conjugate and Lagrange dualities for composite optimization problems within the framework of abstract convexity. We provide conditions for zero duality gap in conjugate duality. For Lagrange duality, intersection property is applied to obtain zero duality gap. Connection between Lagrange dual and conjugate dual is also established. Examples related to convex and weakly convex functions are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-06T02:00:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "composite optimization problem",
      "abstract convexity",
      "zero duality gap",
      "lagrange duality",
      "study conjugate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}