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Peer-reviewedCC BY 4.0PLOS One

Finite-time and predefined-time dynamical systems for solving strongly pseudomonotone mixed equilibrium problems

  • Qian Wen1
  • Vajahat Karim Khan2
  • Qing-Bo Cai3
  • Md. Kalimuddin Ahmad
  1. 1Fujian Key Laboratory of Big Data Application and Intellectualization for Tea Industry, College of Mathematics and Computer, Wuyi University, Nanping, Fujian, China
  2. 2Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh, Uttar Pradesh, India
  3. 3Fujian 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
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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.

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Cite

BibTeXRIS
BibTeX
@article{wen2026finitetime,
  title = {{Finite-time and predefined-time dynamical systems for solving strongly pseudomonotone mixed equilibrium problems}},
  author = {Qian Wen and Vajahat Karim Khan and Qing-Bo Cai and Md. Kalimuddin Ahmad},
  journal = {PLOS One},
  year = {2026},
  month = sep,
  doi = {10.1371/journal.pone.0357046},
  url = {https://doi.org/10.1371/journal.pone.0357046},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Finite-time and predefined-time dynamical systems for solving strongly pseudomonotone mixed equilibrium problems
AU  - Qian Wen
AU  - Vajahat Karim Khan
AU  - Qing-Bo Cai
AU  - Md. Kalimuddin Ahmad
PY  - 2026
DA  - 2026/09/01
JO  - PLOS One
DO  - 10.1371/journal.pone.0357046
UR  - https://doi.org/10.1371/journal.pone.0357046
AB  - 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.
SN  - 1932-6203
ER  -