Consider . Suppose is maximized, subject to and , at . If the are differentiable, then the Gibbs lemma states that there exists a such that
- J. M. Danskin (6 December 2012). The Theory of Max-Min and its Application to Weapons Allocation Problems. Springer Science & Business Media. ISBN 978-3-642-46092-0.
... problems in which one side must make his move knowing that the other side will then learn what the move is and optimally counter. They are fundamental in particular to military weapons-selection problems involving large systems...