2 GENERALIZATIONS OF DYKSTRA CYCLIC PROJECTIONS ALGORITHM

Authors
HUNDAL H DEUTSCH F
Citation
H. Hundal et F. Deutsch, 2 GENERALIZATIONS OF DYKSTRA CYCLIC PROJECTIONS ALGORITHM, Mathematical programming, 77(3), 1997, pp. 335-355
Citations number
16
Categorie Soggetti
Operatione Research & Management Science",Mathematics,"Operatione Research & Management Science",Mathematics,"Computer Science Software Graphycs Programming
Journal title
Mathematical programming → ACNP
ISSN journal
00255610
Volume
77
Issue
3
Year of publication
1997
Pages
335 - 355
Database
ISI
SICI code
0025-5610(1997)77:3<335:2GODCP>2.0.ZU;2-E
Abstract
Dykstra's cyclic projections algorithm allows one to compute best appr oximations to any point x in a Hilbert space from the intersection C = boolean AND(1)(r) C-i of a finite number of closed convex sets C-i, b y reducing it to a sequence of best approximation problems from the in dividual sets Ci. Here we present two generalizations of this algorith m. First we allow the number of sets Ci to be infinite rather than fin ite; secondly, we allow a random, rather than cyclic, ordering of the sets C-1. (C) 1997 The Mathematical Programming Society, Inc.