{
  "annotation_id": "fea2c516-9ad9-48d9-9320-373340eb3bea",
  "date_created": "2026-02-17T05:53:08.152000Z",
  "date_modified": "2026-02-17T05:53:08.152000Z",
  "file_hash": "ee3247218dc9ed9ebc088c8234cd30a7e0f4bf1ca4da445c8eca153bdba53a9a",
  "private": false,
  "record": {
    "abstract": "This paper addresses the minimization of a finite sum of prox-convex functions under Lipschitz continuity of each component. We propose two variants of the splitting proximal point algorithms proposed in \\cite{Bacak,Bertsekas}: one deterministic with a fixed update order, and one stochastic with random sampling, and we extend them from convex to prox-convex functions. We prove global convergence for both methods under standard stepsize a\\-ssump\\-tions, with almost sure convergence for the stochastic variant via supermartingale theory. Numerical experiments with nonconvex quadratic functions illustrate the efficiency of the proposed methods and support the theoretical results.",
    "arxiv_id": "2601.06970",
    "authors": [
      "Jose de Brito",
      "Felipe Lara",
      "Tran Van Thang"
    ],
    "categories": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "title": "Splitting Proximal Point Algorithms for the Sum of Prox-Convex Functions",
    "url": "https://arxiv.org/abs/2601.06970",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "60339383-b981-4553-bc44-a34d948d0da9",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}