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Linear convergence of first order methods for non-strongly convex optimization

Author

Listed:
  • Ion Necoara
  • Yurii Nesterov
  • François Glineur

Abstract

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Suggested Citation

  • Ion Necoara & Yurii Nesterov & François Glineur, 2019. "Linear convergence of first order methods for non-strongly convex optimization," LIDAM Reprints CORE 3000, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3000
    Note: In : Mathematical Programming A, 175, 69, 107, 2019
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    Cited by:

    1. Vassilis Apidopoulos & Nicolò Ginatta & Silvia Villa, 2022. "Convergence rates for the heavy-ball continuous dynamics for non-convex optimization, under Polyak–Łojasiewicz condition," Journal of Global Optimization, Springer, vol. 84(3), pages 563-589, November.
    2. Ion Necoara, 2021. "General Convergence Analysis of Stochastic First-Order Methods for Composite Optimization," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 66-95, April.
    3. Ching-pei Lee & Stephen J. Wright, 2019. "Inexact Successive quadratic approximation for regularized optimization," Computational Optimization and Applications, Springer, vol. 72(3), pages 641-674, April.
    4. Hui Zhang & Yu-Hong Dai & Lei Guo & Wei Peng, 2021. "Proximal-Like Incremental Aggregated Gradient Method with Linear Convergence Under Bregman Distance Growth Conditions," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 61-81, February.
    5. Adrien B. Taylor & Julien M. Hendrickx & François Glineur, 2018. "Exact Worst-Case Convergence Rates of the Proximal Gradient Method for Composite Convex Minimization," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 455-476, August.
    6. Huynh Ngai & Ta Anh Son, 2022. "Generalized Nesterov’s accelerated proximal gradient algorithms with convergence rate of order o(1/k2)," Computational Optimization and Applications, Springer, vol. 83(2), pages 615-649, November.
    7. Yunier Bello-Cruz & Guoyin Li & Tran Thai An Nghia, 2022. "Quadratic Growth Conditions and Uniqueness of Optimal Solution to Lasso," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 167-190, July.
    8. Yunier Bello-Cruz & Guoyin Li & Tran T. A. Nghia, 2021. "On the Linear Convergence of Forward–Backward Splitting Method: Part I—Convergence Analysis," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 378-401, February.
    9. Woocheol Choi & Doheon Kim & Seok-Bae Yun, 2022. "Convergence Results of a Nested Decentralized Gradient Method for Non-strongly Convex Problems," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 172-204, October.
    10. Benjamin Grimmer, 2023. "General Hölder Smooth Convergence Rates Follow from Specialized Rates Assuming Growth Bounds," Journal of Optimization Theory and Applications, Springer, vol. 197(1), pages 51-70, April.
    11. Olivier Fercoq & Zheng Qu, 2020. "Restarting the accelerated coordinate descent method with a rough strong convexity estimate," Computational Optimization and Applications, Springer, vol. 75(1), pages 63-91, January.
    12. Zamani, Moslem & Abbaszadehpeivasti, Hadi & de Klerk, Etienne, 2024. "The exact worst-case convergence rate of the alternating direction method of multipliers," Other publications TiSEM f30ae9e6-ed19-423f-bd1e-0, Tilburg University, School of Economics and Management.
    13. Xiaoya Zhang & Wei Peng & Hui Zhang, 2022. "Inertial proximal incremental aggregated gradient method with linear convergence guarantees," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(2), pages 187-213, October.
    14. Wei Peng & Hui Zhang & Xiaoya Zhang & Lizhi Cheng, 2020. "Global complexity analysis of inexact successive quadratic approximation methods for regularized optimization under mild assumptions," Journal of Global Optimization, Springer, vol. 78(1), pages 69-89, September.

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