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Psychometrika

, Volume 55, Issue 3, pp 417–428 | Cite as

Majorization as a tool for optimizing a class of matrix functions

  • Henk A. L. Kiers
Article

Abstract

The problem of minimizing a general matrix, trace function, possibly subject to certain constraints, is approached by means of majorizing this function by one having a simple quadratic shape and whose minimum is easily found. It is shown that the parameter set that minimizes the majorizing function also decreases the matrix trace function, which in turn provides a monotonically convergent algorithm for minimizing the matrix trace function iteratively. Three algorithms based on majorization for solving certain least squares problems are shown to be special cases. In addition, by means of several examples, it is noted how algorithms may be provided for a wide class of statistical optimization tasks for which no satisfactory algorithms seem available.

Key words

trace optimization majorization alternating least squares 

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Copyright information

© The Psychometric Society 1990

Authors and Affiliations

  • Henk A. L. Kiers
    • 1
  1. 1.University of GroningenThe Netherlands

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