The block-wise circumcentered–reflection method

Roger Behling (), J.-Yunier Bello-Cruz () and Luiz-Rafael Santos ()
Additional contact information
Roger Behling: Fundação Getúlio Vargas
J.-Yunier Bello-Cruz: Northern Illinois University
Luiz-Rafael Santos: Federal University of Santa Catarina

Computational Optimization and Applications, 2020, vol. 76, issue 3, No 4, 675-699

Abstract: 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.

Keywords: Accelerating convergence; Best approximation problem; Circumcenter scheme; Douglas–Rachford method; Linear and finite convergence; Method of alternating projections; 49M27; 65K05; 65B99; 90C25 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-019-00155-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:76:y:2020:i:3:d:10.1007_s10589-019-00155-0

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-019-00155-0

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().