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A successive centralized circumcentered-reflection method for the convex feasibility problem

Author

Listed:
  • Roger Behling

    (Fundação Getúlio Vargas
    Federal University of Santa Catarina)

  • Yunier Bello-Cruz

    (Northern Illinois University)

  • Alfredo Iusem

    (Fundação Getúlio Vargas)

  • Di Liu

    (Instituto de Matematica Pura e Aplicada)

  • Luiz-Rafael Santos

    (Federal University of Santa Catarina)

Abstract

In this paper, we present a successive centralization process for the circumcentered-reflection method with several control sequences for solving the convex feasibility problem in Euclidean space. Assuming that a standard error bound holds, we prove the linear convergence of the method with the most violated constraint control sequence. Moreover, under additional smoothness assumptions on the target sets, we establish the superlinear convergence. Numerical experiments confirm the efficiency of our method.

Suggested Citation

  • Roger Behling & Yunier Bello-Cruz & Alfredo Iusem & Di Liu & Luiz-Rafael Santos, 2024. "A successive centralized circumcentered-reflection method for the convex feasibility problem," Computational Optimization and Applications, Springer, vol. 87(1), pages 83-116, January.
    • Handle: RePEc:spr:coopap:v:87:y:2024:i:1:d:10.1007_s10589-023-00516-w
    DOI: 10.1007/s10589-023-00516-w
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    References listed on IDEAS

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    1. WEGGE, Leon L., 1974. "Mean value theorem for convex functions," LIDAM Reprints CORE 185, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Wegge, Leon L., 1974. "Mean value theorem for convex functions," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 207-208, August.
    3. Hui Ouyang & Xianfu Wang, 2021. "Bregman Circumcenters: Basic Theory," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 252-280, October.
    4. Scott B. Lindstrom, 2022. "Computable centering methods for spiraling algorithms and their duals, with motivations from the theory of Lyapunov functions," Computational Optimization and Applications, Springer, vol. 83(3), pages 999-1026, December.
    5. Francisco J. Aragón Artacho & Rubén Campoy & Matthew K. Tam, 2020. "The Douglas–Rachford algorithm for convex and nonconvex feasibility problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(2), pages 201-240, April.
    6. Liqun Qi, 1983. "Complete Closedness of Maximal Monotone Operators," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 315-317, May.
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