Construction of Constrained Optimal Designs

  • Ben Torsney
  • Saumendranath Mandal
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 51)


We consider the problem of finding an ‘approximate’ design maximising a criterion subject to an equality constraint. Initially the Lagrangian is formulated but the Lagrange parameter is removed through a substitution, using linear equation theory, in an approach which transforms the constrained optimisation problem to a problem of maximising two functions of the design weights simultaneously. They have a common maximum of zero which is simultaneously attained at the constrained optimal design weights. This means that established algorithms for finding optimising distributions can be considered. The approach can easily be extended to the case of several constraints, raising the ‘prospect’ of solving an expanded class of problem.


constrained optimal design multiplicative algorithms optimizing distributions directional derivatives Lagrangian theory equivalence theorem 


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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Ben Torsney
    • 1
  • Saumendranath Mandal
    • 1
  1. 1.Department of StatisticsUniversity of GlasgowGlasgowUK

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