We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x 1, . . . , x N ) with certain separability and regularity properties. Assuming that f is continuous on a compact level set, the subsequence convergence of the iterates to a stationary point is shown when either f is pseudoconvex in every pair of coordinate blocks from among N-1 coordinate blocks or f has at most one minimum in each of N-2 coordinate blocks. If f is quasiconvex and hemivariate in every coordinate block, then the assumptions of continuity of f and compactness of the level set may be relaxed further. These results are applied to derive new (and old) convergence results for the proximal minimization algorithm, an algorithm of Arimoto and Blahut, and an algorithm of Han. They are applied also to a problem of blind source separation.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
About this article
Cite this article
Tseng, P. Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization. Journal of Optimization Theory and Applications 109, 475–494 (2001). https://doi.org/10.1023/A:1017501703105
- block coordinate descent
- nondifferentiable minimization
- stationary point
- Gauss–Seidel method
- quasiconvex functions
- pseudoconvex functions