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 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) = x2 grows at too fast a rate away from the origin, but passes the test near it.