{
  "id": "2301.04431",
  "version": "v1",
  "published": "2023-01-11T12:19:28.000Z",
  "updated": "2023-01-11T12:19:28.000Z",
  "title": "Adaptive proximal algorithms for convex optimization under local Lipschitz continuity of the gradient",
  "authors": [
    "Puya Latafat",
    "Andreas Themelis",
    "Lorenzo Stella",
    "Panagiotis Patrinos"
  ],
  "categories": [
    "math.OC"
  ],
  "abstract": "Backtracking linesearch is the de facto approach for minimizing continuously differentiable functions with locally Lipschitz gradient. In recent years, it has been shown that in the convex setting it is possible to avoid linesearch altogether, and to allow the stepsize to adapt based on a local smoothness estimate without any backtracks or evaluations of the function value. In this work we propose an adaptive proximal gradient method, adaPGM, that uses novel tight estimates of the local smoothness modulus which leads to less conservative stepsize updates and that can additionally cope with nonsmooth terms. This idea is extended to the primal-dual setting where an adaptive three term primal-dual algorithm, adaPDM, is proposed which can be viewed as an extension of the PDHG method. Moreover, in this setting the fully adaptive adaPDM$^+$ method is proposed that avoids evaluating the linear operator norm by invoking a backtracking procedure, that, remarkably, does not require extra gradient evaluations. Numerical simulations demonstrate the effectiveness of the proposed algorithm compared to the state of the art.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-11T12:19:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65K05",
      "90C06",
      "90C25",
      "90C30",
      "90C47"
    ],
    "keywords": [
      "local lipschitz continuity",
      "adaptive proximal algorithms",
      "convex optimization",
      "term primal-dual algorithm",
      "local smoothness modulus"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}