saddle point

Neither peak nor valley

A saddle point is a point on a curved surface where the slope is zero but which is neither a maximum nor a minimum—like the center of a horse's saddle, which curves up front-to-back but down side-to-side.

In mathematics and economics, saddle points appear in optimization problems and game theory, marking equilibria where no player gains by changing strategy unilaterally.

geography

mountain pass

Route through highlands

  • colSpreadsheet vertical section
  • ridgeNarrow raised strip
  • valleyLow ground between heights

watershed · elevation · terrain · topography · contour · divide · notch · gap · alpine · trail junction

mathematics

inflection

Word form alteration

calculus · surface · tangent plane · eigenvalues · extremum · local minimum · local maximum · concavity

optimization

minimax

Worst-case loss reduction

neural network · learning rate · escape · plateau · barrier · search algorithm · momentum · basin · trajectory

gametheory

minimax

Worst-case loss reduction

optimal play

economics

equilibrium

State of balance

Categories
Opposites
mathematical extrema type

saddle pointlocal maximum

Highest nearby, not overall

local minimum · global maximum · extremum · peak · valley

optimization stability

saddle pointstable equilibrium

Self-correcting balanced state

attractor · convergence point

surface curvature character

saddle pointbowl

Concave food container

dome · cup · cap

Family

saddle, point, saddled, saddlebag, saddlebags, saddling, saddler, saddlery, unsaddle

Familiarity
Top 500,000
Profile
Used worldwide · Timeless · Rated G