Optimal convergence rates for generalized alternating projections

Mattias Fält, Pontus Giselsson

Forskningsoutput: Kapitel i bok/rapport/Conference proceedingKonferenspaper i proceedingPeer review

Sammanfattning

Generalized alternating projections is an algorithm that alternates relaxed projections onto a finite number of sets to find a point in their intersection. We consider the special case of two linear subspaces, for which the algorithm reduces to matrix multiplications. For convergent powers of the matrix, the asymptotic rate is linear and decided by the magnitude of the subdominant eigenvalue. In this paper, we show how to select the three algorithm parameters to optimize this magnitude, and hence the asymptotic convergence rate. The obtained rate depends on the Friedrichs angle between the subspaces and is considerably better than known rates for other methods such as alternating projections and DouglasRachford splitting. We also present an adaptive scheme that, online, estimates the Friedrichs angle and updates the algorithm parameters based on this estimate. A numerical example is provided that supports our theoretical claims and shows very good performance for the adaptive method.
Originalspråkengelska
Titel på värdpublikationProceedings of the IEEE Conference on Decision and Control, 2017
FörlagIEEE - Institute of Electrical and Electronics Engineers Inc.
Sidor2268-2274
Antal sidor7
ISBN (elektroniskt)978-1-5090-2873-3
ISBN (tryckt)978-1-5090-2874-0
DOI
StatusPublished - 2017 dec. 12
Evenemang56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australien
Varaktighet: 2017 dec. 122017 dec. 15
Konferensnummer: 56
http://cdc2017.ieeecss.org/

Konferens

Konferens56th IEEE Annual Conference on Decision and Control, CDC 2017
Förkortad titelCDC 2017
Land/TerritoriumAustralien
OrtMelbourne
Period2017/12/122017/12/15
Internetadress

Ämnesklassifikation (UKÄ)

  • Reglerteknik

Fingeravtryck

Utforska forskningsämnen för ”Optimal convergence rates for generalized alternating projections”. Tillsammans bildar de ett unikt fingeravtryck.

Citera det här