A modified forward-backward splitting method for maximal monotone mappings

Authors
Citation
P. Tseng, A modified forward-backward splitting method for maximal monotone mappings, SIAM J CON, 38(2), 2000, pp. 431-446
Citations number
61
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics,"Engineering Mathematics
Journal title
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN journal
0363-0129 → ACNP
Volume
38
Issue
2
Year of publication
2000
Pages
431 - 446
Database
ISI
SICI code
0363-0129(20000202)38:2<431:AMFSMF>2.0.ZU;2-W
Abstract
We consider the forward-backward splitting method for finding a zero of the sum of two maximal monotone mappings. This method is known to converge whe n the inverse of the forward mapping is strongly monotone. We propose a mod ification to this method, in the spirit of the extragradient method for mon otone variational inequalities, under which the method converges assuming o nly the forward mapping is (Lipschitz) continuous on some closed convex sub set of its domain. The modification entails an additional forward step and a projection step at each iteration. Applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed.