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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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