saddle point
A "saddle point" gets its name from the visual resemblance to a horse's saddle, where the function curves up in one direction and down in another.
Definition
C1Mathematics
(technical, academic)A critical point on a function's graph where the slopes in perpendicular directions are zero, but it is neither a local maximum nor a local minimum.
Example
- The function has a saddle point at (0,0) because the slopes in the x and y directions are zero, but it is not an extremum.
C1Game Theory
(technical, academic)A situation in a payoff matrix where neither player's chosen strategy can be improved unilaterally.
Example
- In this game, the saddle point ensures that both players are making optimal decisions.
C1Optimization
(technical, academic)A point where a function has a minimum along one direction and a maximum along another.
Example
- During optimization, the algorithm identified a saddle point, indicating mixed behavior in different directions.
Similar
Terms that have similar or relatively close meanings to "saddle point":
critical pointextreme pointinflection pointfixed pointdouble pointsaddle seatsaddle jointpivot pointtransition pointhigh pointsaddle reef