= Lipschitz Continuity =

'''Lipschitz continuity''' is a restriction placed upon a function. A function is Lipschitz continuous if its rate of change is bounded.

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== Description ==

In terms of [[LinearAlgebra/Distance|Euclidean distance]], a function ''f'' is Lipschitz continuous if there is a constant ''K'' such that ''||f(x) - f(y)|| <= K ||x - y||''. ''K'' is referred to as the '''Lipschitz constant'''.

Note that this does differ from constraints defined in terms of differentiability. As an example: the absolute value function is Lipschitz continuous, but is ''not'' differentiable everywhere.

A function can be ''locally'' Lipschitz continuous without being ''globally'' so. ''f(x) = x^2^'' grows at too fast a rate away from the origin, but passes the test near it.



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CategoryRicottone