A Lagrangian approach to optimal design
| Autor: | S. D. Silvey, D. M. Titterington |
|---|---|
| Rok vydání: | 1974 |
| Předmět: |
Statistics and Probability
Optimal design Concave function Applied Mathematics General Mathematics Object (computer science) Agricultural and Biological Sciences (miscellaneous) Prime (order theory) Set (abstract data type) Combinatorics Transpose Line (geometry) Symmetric matrix Statistics Probability and Uncertainty General Agricultural and Biological Sciences Mathematics |
| Zdroj: | Biometrika. 61:299-302 |
| ISSN: | 1464-3510 0006-3444 |
| DOI: | 10.1093/biomet/61.2.299 |
| Popis: | where u is a column vector of k components and prime denotes transpose. The D-optimal design problem is to determine a A which maximizes log det M(A). Now log det is a concave function on the set of nonnegative-definite symmetric matrices and so the D-optimal problem can be regarded as a particular case of the following one, which we shall call the qs-optimal design problem: given a concave function q6 on the nonnegativedefinite symmetric k x k matrices, determine A to maximize q{M(A)}. Recently, one line of research has shown that much of the highly developed theory of D-optimal design can be generalized to qs-optimal design (Fedorov, 1972, Chapter 2; Kiefer, 1974; Whittle, 1973). Another has shown how Lagrangian theory can be exploited in the D-optimal design area (Silvey, 1972; Sibson, 1972a, b; Silvey & Titterington, 1973). It is the object of the present note to develop the Lagrangian approach to the q6optimal problem. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|