Monitoring distributed parameters systems : Necessary conditions for optimality

Necessary conditions for optimality
Monitoring distributed parameters systems

Author : Jean-Pierre YVON

Publication date: April 10, 2009 | Lire en français

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3. Necessary conditions for optimality

3.1 Directional derivatives

As with variational calculus problems, optimality conditions are obtained by introducing the concept of directional derivatives, which replace the partial derivatives used in optimization. In what follows, $U$ is a real Hilbert space, it will be the "control space," equipped with a scalar product denoted by ${〈 ., . 〉}_{}$

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