Journal of Optimization Theory and Applications

, Volume 54, Issue 3, pp 471–477

Local convergence analysis of a grouped variable version of coordinate descent

  • J. C. Bezdek
  • R. J. Hathaway
  • R. E. Howard
  • C. A. Wilson
  • M. P. Windham
Contributed Papers

DOI: 10.1007/BF00940196

Cite this article as:
Bezdek, J.C., Hathaway, R.J., Howard, R.E. et al. J Optim Theory Appl (1987) 54: 471. doi:10.1007/BF00940196


LetF(x,y) be a function of the vector variablesxRn andyRm. One possible scheme for minimizingF(x,y) is to successively alternate minimizations in one vector variable while holding the other fixed. Local convergence analysis is done for this vector (grouped variable) version of coordinate descent, and assuming certain regularity conditions, it is shown that such an approach is locally convergent to a minimizer and that the rate of convergence in each vector variable is linear. Examples where the algorithm is useful in clustering and mixture density decomposition are given, and global convergence properties are briefly discussed.

Key Words

Coordinate descentlocal linear convergence

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • J. C. Bezdek
    • 1
  • R. J. Hathaway
    • 2
  • R. E. Howard
    • 3
  • C. A. Wilson
    • 4
  • M. P. Windham
    • 5
  1. 1.Department of Computer ScienceUniversity of South CarolinaColumbia
  2. 2.Department of StatisticsUniversity of South CarolinaColumbia
  3. 3.Department of MathematicsUniversity of South CarolinaColumbia
  4. 4.Department of MathematicsWinthrop CollegeRock Hill
  5. 5.Department of MathematicsUtah State UniversityLogan