{
  "abstract": "In this paper, we propose a class of proximal dynamical systems (PDSs) with finite-time (FT) stability and predefined-time (PdT) stability for solving strongly pseudomonotone mixed equilibrium problems (MEPs) in Hilbert spaces. Unlike existing approaches for variational inequalities and standard equilibrium problems, the proposed framework is developed specifically for MEPs and provides two distinct dynamical models with FT and PdT convergence. Under the assumptions of strong pseudomonotonicity and Lipschitz-type continuity, we establish the existence and uniqueness of the equilibrium solution, prove the global exponential stability of the associated continuous-time nominal system, and show that its discrete-time discretization yields a proximal-type algorithm with linear convergence. Furthermore, we construct an FT stable PDS whose equilibrium point coincides with the solution of the MEP and derive sufficient conditions for finite-time convergence. In addition, we introduce a novel PdT dynamical system that guarantees convergence within a prescribed time independent of the initial conditions. Numerical experiments are provided to demonstrate the effectiveness of the proposed methods, indicating that the PdT system achieves faster convergence compared to the nominal and FT systems. Finally, an application to sparse signal recovery in compressed sensing demonstrates the practical effectiveness of the proposed PdT scheme.",
  "abstract_shown": true,
  "affiliations": [
    "Fujian Key Laboratory of Big Data Application and Intellectualization for Tea Industry, College of Mathematics and Computer, Wuyi University, Nanping, Fujian, China",
    "Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, Uttar Pradesh, India",
    "Fujian Provincial Key Laboratory of Data-Intensive Computing, Key Laboratory of Intelligent Computing and Information Processing, School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, Fujian, China"
  ],
  "article_type": "Research Article",
  "arxiv": null,
  "author_total": 4,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Qian Wen"
    },
    {
      "affs": [
        1
      ],
      "name": "Vajahat Karim Khan"
    },
    {
      "affs": [
        2
      ],
      "name": "Qing-Bo Cai"
    },
    {
      "name": "Md. Kalimuddin Ahmad"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vx8j7asqw21r.bib",
  "cited_by": 0,
  "doi": "10.1371/journal.pone.0357046",
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  "id": "1vx8j7asqw21r",
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    "1932-6203"
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  "landing_url": "https://doi.org/10.1371/journal.pone.0357046",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
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      "1703|Optimization and Variational Analysis"
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      "/Computer and information sciences/Software engineering/Source code"
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      "/Physical sciences/Mathematics/Systems science/Dynamical systems"
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      "plos",
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  "pdf_url": "https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0357046&type=printable",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": "Public Library of Science",
  "ris": "https://research.draconitic.com/paper/1vx8j7asqw21r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:02Z",
      "native_id": "10.1371/journal.pone.0357046",
      "source": "plos",
      "url": "https://doi.org/10.1371/journal.pone.0357046"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "plos:dynamical systems",
      "subfield": "dynamical-systems"
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    {
      "field": "mathematics",
      "origin": "plos:statistics",
      "subfield": "statistics"
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  ],
  "title": "Finite-time and predefined-time dynamical systems for solving strongly pseudomonotone mixed equilibrium problems",
  "title_text": "Finite-time and predefined-time dynamical systems for solving strongly pseudomonotone mixed equilibrium problems",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:02Z",
  "url": "https://research.draconitic.com/paper/1vx8j7asqw21r",
  "venue": "PLOS One",
  "versions": []
}