{
  "annotation_id": "52581c32-9d38-4552-8f31-33684bc72b68",
  "date_created": "2026-02-17T05:53:08.042000Z",
  "date_modified": "2026-02-17T05:53:08.042000Z",
  "file_hash": "5f1cd09f619e9d27b771943fed29e712793595808439fc3f00243e7d1d635a52",
  "private": false,
  "record": {
    "abstract": "In this paper, we design and apply novel inexact adaptive algorithms to deal with minimizing difference-of-convex (DC) functions in Hilbert spaces. We first introduce I-ADCA, an inexact adaptive counterpart of the well-recognized DCA (difference-of-convex algorithm), that allows inexact subgradient evaluations and inexact solutions to convex subproblems while still guarantees global convergence to stationary points. Under a Polyak-Lojasiewicz type property for DC objectives, we obtain explicit convergence rates for the proposed algorithm. Our main application addresses elliptic optimal control problems with control constraints and nonconvex $L^{1-2}$ sparsity-enhanced regularizers admitting a DC decomposition. Employing I-ADCA and appropriate versions of finite element discretization leads us to an efficient procedure for solving such problems with establishing its well-posedness and error bound estimates confirmed by numerical experiments.",
    "arxiv_id": "2601.06622",
    "authors": [
      "P. D. Khanh",
      "V. V. H. Khoa",
      "B. S. Mordukhovich",
      "D. B. Tran",
      "N. V. Vo"
    ],
    "categories": [
      "math.OC"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "title": "Inexact DC Algorithms in Hilbert Spaces with Applications to PDE-Constrained Optimization",
    "url": "https://arxiv.org/abs/2601.06622",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "60d2230d-a157-41f7-b56c-c5a318a270bf",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}