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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


For a regular optimality criterion function $\Phi$, a sequence of design measures $\{\xi_n\}$ is generated using the iteration $\xi_{n+1} = (1 - \alpha_n)\xi_n + \alpha_n\xi_n$, where $\xi_n$ is chosen to minimize $\nabla \Phi(M(\xi_n), M(\xi))$ over all $\xi$ and $\{\alpha_n\}$ is a prescribed sequence of numbers from (0, 1). This is called a general step-length algorithm for $\Phi$. Typical conditions on $\{\alpha_n\}$ are $\alpha_n \rightarrow 0$ and $\Sigma_n\alpha_n = \infty$. In this paper, a dichotomous behavior of $\{\xi_n\}$ is proved under the above conditions on $\{\alpha_n\}$ for $\Phi$ satisfying some mild regularity conditions. Sufficient conditions for convergence to optimal designs are also established. This can be applied to show that the $\{\xi_n\}$ as constructed above do converge to an optimal design for most of the trace-related and determinant-related design criteria.


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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.


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

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

Primary: 62K05
Secondary: 62L05

Keywords: $\Phi_p$-optimality , $A$-optimality , $D$-optimality , $D_s$-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
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