The circumcentered-reflection method achieves better rates than alternating projections

Reza Arefidamghani (), Roger Behling (), Yunier Bello-Cruz (), Alfredo N. Iusem () and Luiz-Rafael Santos ()
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Reza Arefidamghani: Instituto de Matemática Pura e Aplicada
Roger Behling: Fundação Getúlio Vargas
Yunier Bello-Cruz: Northern Illinois University
Alfredo N. Iusem: Instituto de Matemática Pura e Aplicada
Luiz-Rafael Santos: Federal University of Santa Catarina

Computational Optimization and Applications, 2021, vol. 79, issue 2, No 9, 507-530

Abstract: Abstract We study the convergence rate of the Circumcentered-Reflection Method (CRM) for solving the convex feasibility problem and compare it with the Method of Alternating Projections (MAP). Under an error bound assumption, we prove that both methods converge linearly, with asymptotic constants depending on a parameter of the error bound, and that the one derived for CRM is strictly better than the one for MAP. Next, we analyze two classes of fairly generic examples. In the first one, the angle between the convex sets approaches zero near the intersection, so that the MAP sequence converges sublinearly, but CRM still enjoys linear convergence. In the second class of examples, the angle between the sets does not vanish and MAP exhibits its standard behavior, i.e., it converges linearly, yet, perhaps surprisingly, CRM attains superlinear convergence.

Keywords: Convex feasibility problem; Alternating projections; Circumcentered-reflection method; Convergence rate; 49M27; 65K05; 65B99; 90C25 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-021-00275-6

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