Construction of Constrained Optimal Designs
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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.
Keywordsconstrained optimal design multiplicative algorithms optimizing distributions directional derivatives Lagrangian theory equivalence theorem
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