Some guidelines for constructing exact d-optimal designs on convex design spaces

Mark E. Johnson; Christopher J. Nachtsheim

doi:10.1080/00401706.1983.10487880

Some guidelines for constructing exact d-optimal designs on convex design spaces

Mark E. Johnson, Christopher J. Nachtsheim

Research output: Contribution to journal › Article › peer-review

78 Scopus citations

Abstract

Some problems unique to the construction of N-point D-optimal designs on convex design spaces are considered. Multiple-point augmentation and exchange algorithms are shown to be more costly and less efficient than the analogous single-point procedures. Moreover, some recommendations for improving single-point methods are given. Finally, empirical evidence is found that supports the Galil and Kiefer option for constructing initial designs and Powell's optimization method for design augmentation.

Original language	English (US)
Pages (from-to)	271-277
Number of pages	7
Journal	Technometrics
Volume	25
Issue number	3
DOIs	https://doi.org/10.1080/00401706.1983.10487880
State	Published - Aug 1983
Externally published	Yes

Bibliographical note

Funding Information:
The authors would like to thank the refereesa nd the editor for suggestionst hat led to a much improved presentation. The authors are also indebted to Dennis Cook for helpful comments during the course of their research,a nd to James Evans for help in implementing the modified simplex algorithm. This work was partially performed under the auspiceso f the United States Department of Energy (Contract w-7405- ENG.36).

Keywords

Conjugate directions
D-optimal
Design augmentation
Exchange algorithm
Nonlinear optimization
Simplex search

Publisher link

10.1080/00401706.1983.10487880

Find It

Find It at U of M Libraries

Cite this

@article{9bece006afac4c8b8b1eb4e14dbc29d6,

title = "Some guidelines for constructing exact d-optimal designs on convex design spaces",

abstract = "Some problems unique to the construction of N-point D-optimal designs on convex design spaces are considered. Multiple-point augmentation and exchange algorithms are shown to be more costly and less efficient than the analogous single-point procedures. Moreover, some recommendations for improving single-point methods are given. Finally, empirical evidence is found that supports the Galil and Kiefer option for constructing initial designs and Powell's optimization method for design augmentation.",

keywords = "Conjugate directions, D-optimal, Design augmentation, Exchange algorithm, Nonlinear optimization, Simplex search",

author = "Johnson, {Mark E.} and Nachtsheim, {Christopher J.}",

note = "Funding Information: The authors would like to thank the refereesa nd the editor for suggestionst hat led to a much improved presentation. The authors are also indebted to Dennis Cook for helpful comments during the course of their research,a nd to James Evans for help in implementing the modified simplex algorithm. This work was partially performed under the auspiceso f the United States Department of Energy (Contract w-7405- ENG.36).",

year = "1983",

month = aug,

doi = "10.1080/00401706.1983.10487880",

language = "English (US)",

volume = "25",

pages = "271--277",

journal = "Technometrics",

issn = "0040-1706",

publisher = "American Statistical Association",

number = "3",

}

TY - JOUR

T1 - Some guidelines for constructing exact d-optimal designs on convex design spaces

AU - Johnson, Mark E.

AU - Nachtsheim, Christopher J.

N1 - Funding Information: The authors would like to thank the refereesa nd the editor for suggestionst hat led to a much improved presentation. The authors are also indebted to Dennis Cook for helpful comments during the course of their research,a nd to James Evans for help in implementing the modified simplex algorithm. This work was partially performed under the auspiceso f the United States Department of Energy (Contract w-7405- ENG.36).

PY - 1983/8

Y1 - 1983/8

N2 - Some problems unique to the construction of N-point D-optimal designs on convex design spaces are considered. Multiple-point augmentation and exchange algorithms are shown to be more costly and less efficient than the analogous single-point procedures. Moreover, some recommendations for improving single-point methods are given. Finally, empirical evidence is found that supports the Galil and Kiefer option for constructing initial designs and Powell's optimization method for design augmentation.

AB - Some problems unique to the construction of N-point D-optimal designs on convex design spaces are considered. Multiple-point augmentation and exchange algorithms are shown to be more costly and less efficient than the analogous single-point procedures. Moreover, some recommendations for improving single-point methods are given. Finally, empirical evidence is found that supports the Galil and Kiefer option for constructing initial designs and Powell's optimization method for design augmentation.

KW - Conjugate directions

KW - D-optimal

KW - Design augmentation

KW - Exchange algorithm

KW - Nonlinear optimization

KW - Simplex search

UR - http://www.scopus.com/inward/record.url?scp=0020799674&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0020799674&partnerID=8YFLogxK

U2 - 10.1080/00401706.1983.10487880

DO - 10.1080/00401706.1983.10487880

M3 - Article

AN - SCOPUS:0020799674

SN - 0040-1706

VL - 25

SP - 271

EP - 277

JO - Technometrics

JF - Technometrics

IS - 3

ER -

Some guidelines for constructing exact d-optimal designs on convex design spaces

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this