Definiton. Saddle point

• \(a = (a^{1}, \ldots, a^{n}) \in \mathbb{R}^{n}\),
• \(f: \mathbb{R}^{n} \rightarrow \mathbb{R}\),

$a$ is said to be saddle point of $f$ if \(g_{x}(t) := (a + xt)\), \(h_{y}(t) := (a + yt)\)

• \(\forall x \neq 0\), \(g_{x}(t)\) local maximum.
• \(\forall x \neq 0\), \(h_{x}(t)\) local minimum.

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