Local convergence analysis of a grouped variable version of coordinate descent |
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Authors: | J C Bezdek R J Hathaway R E Howard C A Wilson M P Windham |
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Institution: | (1) Department of Computer Science, University of South Carolina, Columbia, South Carolina;(2) Department of Statistics, University of South Carolina, Columbia, South Carolina;(3) Department of Mathematics, University of South Carolina, Columbia, South Carolina;(4) Department of Mathematics, Winthrop College, Rock Hill, South Carolina;(5) Department of Mathematics, Utah State University, Logan, Utah |
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Abstract: | LetF(x,y) be a function of the vector variablesxR
n
andyR
m
. 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.This research was supported in part by NSF Grant No. IST-84-07860. The authors are indebted to Professor R. A. Tapia for his help in improving this paper. |
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Keywords: | Coordinate descent local linear convergence |
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