Journal of Optimization Theory and Applications

, Volume 109, Issue 3, pp 475–494

Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization

  • P. Tseng
Article

DOI: 10.1023/A:1017501703105

Cite this article as:
Tseng, P. Journal of Optimization Theory and Applications (2001) 109: 475. doi:10.1023/A:1017501703105

Abstract

We study the convergence properties of a (block) coordinate descent method applied to minimize a nondifferentiable (nonconvex) function f(x1, . . . , xN) 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.

block coordinate descent nondifferentiable minimization stationary point Gauss–Seidel method convergence quasiconvex functions pseudoconvex functions 

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • P. Tseng
    • 1
  1. 1.Department of MathematicsUniversity of WashingtonSeattle

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