Convergence of a block coordinate descent method for nondifferentiable minimization

Authors
Citation
P. Tseng, Convergence of a block coordinate descent method for nondifferentiable minimization, J OPTIM TH, 109(3), 2001, pp. 475-494
Citations number
38
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Engineering Mathematics
Journal title
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
ISSN journal
0022-3239 → ACNP
Volume
109
Issue
3
Year of publication
2001
Pages
475 - 494
Database
ISI
SICI code
0022-3239(200106)109:3<475:COABCD>2.0.ZU;2-8
Abstract
We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x(I),..., x( n)) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence of the iter ates to a stationary point is shown when either f is pseudoconvex in every pair of coordinate blocks from among N - 1 coordinate blocks orf has at mos t one minimum in each of N - 2 coordinate blocks. If f is quasiconvex and h emivariate in every coordinate block, then the assumptions of continuity of f and compactness of the level set may be relaxed further. These results ar e applied to derive new land old) convergence results for the proximal mini mization algorithm, an algorithm of Arimoto and Blahut, and an algorithm of Han. They are applied also to a problem of blind source separation.