Saddle Point

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saddle point

[′sad·əl ‚pȯint]
A point where all the first partial derivatives of a function vanish but which is not a local maximum or minimum.
For a matrix of real numbers, an element that is both the smallest element of its row and the largest element of its column, or vice versa.
For a two-person, zero-sum game, an element of the payoff matrix that is the smallest element of its row and the largest element of its column, so that the corresponding strategies are optimal for each player, given the strategy chosen by the other player.

Saddle Point


a critical point of a first-order differential equation. In a neighborhood of a saddle point, four half-line integral

Figure 1

curves enter the critical point. Between the four curves there are four regions, each of which contains a family of integral curves resembling hyperbolas (see Figure l). The pattern of integral curves in a neighborhood of a saddle point is reminiscent of the contour lines of a hyperbolic paraboloid, which has the shape of a saddle—hence the name of the critical point.

References in periodicals archive ?
This leads us to an infinite number of saddle points (cf.
2], One important fact in case d"(c) < 0 is that these critical points arc saddle points but not local minimum, in contrast with the case d"(c) > 0, where these critical points arc in fact local minimum.
The main idea of our method is to insert saddle points and connect them to the corner vertices of a cube to generate tetrahedra.
The next relevant saddle points are w [+ or -] 1, which will give the closest singularities of dv/dw to the origin in the w variable.
Finding the critical points of a function includes finding all local maxima, local minima, and saddle points.
Mishra, Lagrange multipliers saddle points and scalarizations in composite multiobjective nonsmooth programming, Optimization.
Even for such a simple walk, the analysis turns out to be quite sophisticated and it involves Mellin transforms, Tauberian theorems, and infinite number of saddle points.
ij]])m x n has no saddle points mixed strategies must be used.
Perfect-foresight saddle points, on the other hand, are stable under learning and should be retained.
In the aforementioned techniques, the HOs all meet the characteristics that the saddle points are symmetric about a center point.