{
  "annotation_id": "edf0f84e-8d2b-4c97-92dd-44c0794e43f6",
  "date_created": "2026-02-17T05:53:20.472000Z",
  "date_modified": "2026-02-17T05:53:20.472000Z",
  "file_hash": "04db090f2a35f4bd1f30941ef7ed0287d77f80ba6d4e6917a6a1eec85cec9022",
  "private": false,
  "record": {
    "abstract": "In [R. J. Baraldi and D. P. Kouri, Math. Program., 201:1 (2023), pp. 559-598], the authors introduced a trust-region method for minimizing the sum of a smooth nonconvex and a nonsmooth convex function, the latter of which has an analytical proximity operator. While many functions satisfy this criterion, e.g., the $\\ell_1$-norm defined on $\\ell_2$, many others are precluded by either the topology or the nature of the nonsmooth term. Using the $\\delta$-Fr\\\u0027echet subdifferential, we extend the definition of the inexact proximity operator and enable its use within the aforementioned trust-region algorithm. Moreover, we augment the analysis for the standard trust-region convergence theory to handle proximity operator inexactness with weighted inner products. We first introduce an algorithm to generate a point in the inexact proximity operator and then apply the algorithm within the trust-region method to solve an optimal control problem constrained by Burgers\u0027 equation.",
    "arxiv_id": "2601.09024",
    "authors": [
      "Leandro Farias Maia",
      "Robert Baraldi",
      "Drew P. Kouri"
    ],
    "categories": [
      "math.OC",
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "An Inexact Weighted Proximal Trust-Region Method",
    "url": "https://arxiv.org/abs/2601.09024",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5f5f2f7c-cdc5-4633-847a-d62bea36e41d",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}