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Variational Calculus in the Space of Measures and Optimal Design

  • Ilya Molchanov
  • Sergei Zuyev
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 51)

Abstract

The paper applies abstract optimisation principles in the space of measures within the context of optimal design problems. It is shown that within this framework it is possible to treat various design criteria and constraints in a unified manner providing a “universal” variant of the Kiefer-Wolfowitz theorem and giving a full spectrum of optimality criteria for particular cases. The described steepest descent algorithm uses the true direction of steepest descent and descends faster than the conventional sequential algorithms that involve renormalisation at every step.

Keywords

design of experiments gradient methods optimal design regression space of measures 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Ilya Molchanov
    • 1
  • Sergei Zuyev
    • 2
  1. 1.Department of StatisticsUniversity of GlasgowUK
  2. 2.Department of Statistics and Modelling ScienceUniversity of StrathclydeUK

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