Definition:Saddle Point

Disambiguation

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Saddle Point may refer to:

Saddle Point (Game Theory)

Let $G$ be a two-player zero-sum game.

Let $G$ be defined by a payoff table $T$.

Let $E$ be an entry in $T$ such that:

$E$ is the smallest entry in its row

$E$ is the largest entry in its column.

Then $E$ is a saddle point of $G$.

Saddle Point (Geometry)

Let $\SS$ be a surface defined by the Cartesian equation $z = \map f {x, y}$.

Let $P$ be a point on $\SS$ such that:

the partial derivatives $\dfrac {\partial z} {\partial x}$ and $\dfrac {\partial z} {\partial y}$ are both zero

but:

there is no local maximum or local minimum at $P$.

Then $P$ is a saddle point of $\SS$.