Statistics, Testing, and Defense Acquisition: Background Papers by National Research Council

Author:National Research Council
Language: eng
Format: epub
Tags: Conflict and Security Issues : Military and Defense Studies
Publisher: NATIONAL ACADEMY PRESS
Published: 1999-08-16T00:00:00+00:00

where are positive weights. Then for A > 1,

and for A < 1,

Proof: We show, by Lagrangian methods, that the bounds in (3.21) and (3.22) are the values associated with the unique critical points of the function in each case. Then, an easy geometric argument involving hyperplanes above or below the surface in (3.20) will demonstrate that these values are extrema. Let

To find critical points of the function under the constraint (3.20), we solve the equations

and

It is evident from the above that there is a single critical point of f, namely

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