Entropic proximal decomposition methods for convex programs and variational inequalities

Citation
A. Auslander et M. Teboulle, Entropic proximal decomposition methods for convex programs and variational inequalities, MATH PROGR, 91(1), 2001, pp. 33-47
Citations number
25
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
MATHEMATICAL PROGRAMMING
ISSN journal
0025-5610 → ACNP
Volume
91
Issue
1
Year of publication
2001
Pages
33 - 47
Database
ISI
SICI code
0025-5610(200110)91:1<33:EPDMFC>2.0.ZU;2-V
Abstract
We consider convex optimization and variational inequality problems with a given separable structure. We propose a new decomposition method for these problems A which combines the recent logarithmic-quadratic proximal theory introduced by the authors with a decomposition method given by Chen-Teboull e for convex problems with particular structure. The resulting method allow s to produce for the first time provably convergent decomposition schemes b ased on C-infinity Lagrangians for solving convex structured problems. Unde r the only assumption that the primal-dual problems have nonempty solution sets, global convergence of the primal-dual sequences produced by the algor ithm is established.