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.