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

Roger Behling (), Yunier Bello-Cruz (), Alfredo Iusem (), Di Liu () and Luiz-Rafael Santos ()
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Roger Behling: Fundação Getúlio Vargas
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

Computational Optimization and Applications, 2024, vol. 87, issue 1, No 3, 83-116

Abstract: 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.

Keywords: Convex feasibility problem; Superlinear convergence; Circumcentered-reflection method; Projection methods; 49M27; 65K05; 65B99; 90C25 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-023-00516-w

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