{
  "id": "2401.04806",
  "version": "v1",
  "published": "2024-01-09T20:33:10.000Z",
  "updated": "2024-01-09T20:33:10.000Z",
  "title": "Characterisation of zero duality gap for optimization problems in spaces without linear structure",
  "authors": [
    "Ewa Bednarczuk",
    "Monika Syga"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2011.09194",
  "categories": [
    "math.OC"
  ],
  "abstract": "We prove sufficient and necessary conditions ensuring zero duality gap for Lagrangian duality in some classes of nonconvex optimization problems. To this aim, we use the $\\Phi$-convexity theory and minimax theorems for $\\Phi$-convex functions. The obtained zero duality results apply to optimization problems involving prox-bounded functions, DC functions, weakly convex functions and paraconvex functions as well as infinite-dimensional linear optimization problems, including Kantorovich duality which plays an important role in determining Wasserstein distance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-09T20:33:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32F17",
      "49J52",
      "49K27",
      "49K35",
      "52A01"
    ],
    "keywords": [
      "linear structure",
      "infinite-dimensional linear optimization problems",
      "necessary conditions ensuring zero duality",
      "convex functions",
      "conditions ensuring zero duality gap"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}