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June, 1987 An Optimization Problem with Applications to Optimal Design Theory
Ching-Shui Cheng
Ann. Statist. 15(2): 712-723 (June, 1987). DOI: 10.1214/aos/1176350370

Abstract

The problem of minimizing $\sum^n_{i = 1}f(x_i)$ subject to the constraints $\sum^n_{i = 1}x_i = A, \sum^n_{i = 1}g(x_i) = B$ and $x_i \geq 0$ is solved. The solutions are different depending upon whether $(\operatorname{sgn} g")f"/g"$ is an increasing or decreasing function. The result is used to show that for certain designs, if they are optimal with respect to two criteria, then they are also optimal with respect to many other criteria.

Citation

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Ching-Shui Cheng. "An Optimization Problem with Applications to Optimal Design Theory." Ann. Statist. 15 (2) 712 - 723, June, 1987. https://doi.org/10.1214/aos/1176350370

Information

Published: June, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0623.62069
MathSciNet: MR888435
Digital Object Identifier: 10.1214/aos/1176350370

Subjects:
Primary: 62K05

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 2 • June, 1987
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