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A Novel Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling

Author

Listed:
  • Xuehui Mei

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830047, China)

  • Pengrui Zhang

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830047, China)

  • Haijun Jiang

    (School of Mathematics and Statistics, YiLi Normal University, Yining 835000, China)

  • Zhiyong Yu

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830047, China)

Abstract

In machine learning, the processing of datasets is an unavoidable topic. One important approach to solving this problem is to design some corresponding algorithms so that they can eventually converge to the optimal solution of the optimization problem. Most existing acceleration algorithms exhibit asymptotic convergence. In order to ensure that the optimization problem converges to the optimal solution within the prescribed time, a novel prescribed-time convergence acceleration algorithm with time rescaling is presented in this paper. Two prescribed-time acceleration algorithms are constructed by introducing time rescaling, and the acceleration algorithms are used to solve unconstrained optimization problems and optimization problems containing equation constraints. Some important theorems are given, and the convergence of the acceleration algorithms is proven using the Lyapunov function method. Finally, we provide numerical simulations to verify the effectiveness and rationality of our theoretical results.

Suggested Citation

  • Xuehui Mei & Pengrui Zhang & Haijun Jiang & Zhiyong Yu, 2025. "A Novel Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling," Mathematics, MDPI, vol. 13(2), pages 1-28, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:251-:d:1566191
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    References listed on IDEAS

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    1. NESTEROV, Yu., 2007. "Gradient methods for minimizing composite objective function," LIDAM Discussion Papers CORE 2007076, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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