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Definition of distance-generating functions and norms.
Functions
Computes the dual of some $norm$.
Euclidean norm.
Mahalanobis distance square. This norm is $1$-strongly convex and $1$-Lipschitz smooth.
Manhattan norm.
Manhattan norm scaled with switching costs.
Negative entropy. $1 / (2 \ln 2)$-strongly convex and $1 / (\delta \ln 2)$-smooth in the $\delta$-interior of the simplex where dimensions sum to $1$. For the $\ell_1$ norm.
Norm squared. $1$-strongly convex and $1$-Lipschitz smooth for the Euclidean norm and the Mahalanobis distance.
Type Definitions
Distance-generating function.
Norm function. Its definition is equivalent to that of a distance-generating function.