Constrained optimal designs
type: Item
instance of: scholarly article
title: Constrained optimal designs
zbMATH Open document ID: 0667.62055
DOI: 10.1016/0378-3758(88)90114-0
author: Carl M.-S. Lee
published in: Journal of Statistical Planning and Inference
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://lib.dr.iastate.edu/cgi/viewcontent.cgi
review text: Consider the usual setting of optimal design theory with a design \(\xi\) given by a discrete measure \(\xi =\{P_ 1,P_ 2,...,P_ n\}\) with support \(\{x_ 1,x_ 2,...,x_ n\}\). Let M(\(\xi)\) be the information matrix of a design \(\xi\) and assume M(\(\xi)\) to be non-singular. The paper tackles the following constrained optimal design problem: Minimize the functional \(\phi\) (M(\(\xi)\)) over the set of all designs with non- singular information matrices subject to \(\phi_ iM(\xi))\leq 0\), \(i=1,2,...,m\), where \(\phi_ 1,\phi_ 2,...,\phi_ m\) are m specified functionals on M(\(\xi)\). Under a set of assumptions on \(\phi\) and the \(\phi_ i's\) the author develops a necessary and sufficient condition for an optimal design using Fréchet derivatives. Some applications of the constrained optimality criterion are presented which include C-restricted D-criterion, multiresponse modeling problem and combination of A- and D-criteria.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 90C90
zbMATH DE Number: 4092599
zbMATH Keywords: convex programming
zbMATH Keywords: Lagrangian function
zbMATH Keywords: Kuhn-Tucker condition
zbMATH Keywords: saddle point
zbMATH Keywords: constrained optimal design problem
zbMATH Keywords: Fréchet derivatives
zbMATH Keywords: C- restricted D-criterion
zbMATH Keywords: multiresponse modeling problem
zbMATH Keywords: combination of A- and D-criteria
reviewed by: B. Leo Raktoe
MaRDI profile type: Publication
OpenAlex ID: W2144767077
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description: scientific article; zbMATH DE number 4092599