Open Access
November, 1978 The Convergence of General Step-Length Algorithms for Regular Optimum Design Criteria
Chien-Fu Wu, Henry P. Wynn
Ann. Statist. 6(6): 1273-1285 (November, 1978). DOI: 10.1214/aos/1176344373

Abstract

For a regular optimality criterion function ΦΦ, a sequence of design measures {ξn}{ξn} is generated using the iteration ξn+1=(1αn)ξn+αnξnξn+1=(1αn)ξn+αnξn, where ξnξn is chosen to minimize Φ(M(ξn),M(ξ))Φ(M(ξn),M(ξ)) over all ξξ and {αn}{αn} is a prescribed sequence of numbers from (0, 1). This is called a general step-length algorithm for ΦΦ. Typical conditions on {αn}{αn} are αn0αn0 and Σnαn=Σnαn=. In this paper, a dichotomous behavior of {ξn}{ξn} is proved under the above conditions on {αn}{αn} for ΦΦ satisfying some mild regularity conditions. Sufficient conditions for convergence to optimal designs are also established. This can be applied to show that the {ξn}{ξn} as constructed above do converge to an optimal design for most of the trace-related and determinant-related design criteria.

Citation

Download Citation

Chien-Fu Wu. Henry P. Wynn. "The Convergence of General Step-Length Algorithms for Regular Optimum Design Criteria." Ann. Statist. 6 (6) 1273 - 1285, November, 1978. https://doi.org/10.1214/aos/1176344373

Information

Published: November, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0396.62059
MathSciNet: MR523762
Digital Object Identifier: 10.1214/aos/1176344373

Subjects:
Primary: 62K05
Secondary: 62L05

Keywords: ΦpΦp-optimality , AA-optimality , DD-optimality , DsDs-optimality , Asymptotic convergence , Convex programming , General step-length algorithms , optimal design algorithms

Rights: Copyright © 1978 Institute of Mathematical Statistics

Vol.6 • No. 6 • November, 1978
Back to Top