The block-wise circumcentered–reflection method
Author ORCID Identifier
Karyn Higgs:https://orcid.org/0000-0001-5433-9729
Alecia Santuzzi:https://orcid.org/0000-0002-9384-4223
Stephen Tonks:https://orcid.org/0000-0002-8219-3517
Ryan Kopatich:https://orcid.org/0000-0002-4133-4280
Publication Title
Computational Optimization and Applications
ISSN
9266003
E-ISSN
15732894
Document Type
Article
Abstract
The elementary Euclidean concept of circumcenter has recently been employed to improve two aspects of the classical Douglas–Rachford method for projecting onto the intersection of affine subspaces. The so-called circumcentered–reflection method is able to both accelerate the average reflection scheme by the Douglas–Rachford method and cope with the intersection of more than two affine subspaces. We now introduce the technique of circumcentering in blocks, which, more than just an option over the basic algorithm of circumcenters, turns out to be an elegant manner of generalizing the method of alternating projections. Linear convergence for this novel block-wise circumcenter framework is derived and illustrated numerically. Furthermore, we prove that the original circumcentered–reflection method essentially finds the best approximation solution in one single step if the given affine subspaces are hyperplanes.
First Page
675
Last Page
699
Publication Date
7-1-2020
DOI
10.1007/s10589-019-00155-0
Keywords
Accelerating convergence, Best approximation problem, Circumcenter scheme, Douglas–Rachford method, Linear and finite convergence, Method of alternating projections
Recommended Citation
Behling, Roger; Bello-Cruz, J.-Yunier; and Santos, Luiz R., "The block-wise circumcentered–reflection method" (2020). NIU Bibliography. 572.
https://huskiecommons.lib.niu.edu/niubib/572
Department
Department of Mathematical Sciences
