What do you mean by Lipschitz condition?
noun Mathematics. the property of a function on a closed interval such that the absolute value of the difference in functional values at any two points in the interval is less than a constant times the absolute value of the difference of the points raised to some positive power m, called the order.
How do you satisfy Lipschitz?
In particular, a function f:[a,b]→R is said to satisfy the Lipschitz condition if there is a constant M such that |f(x)−f(x′)|≤M|x−x′|∀x,x′∈[a,b].
What is the Lipschitz constraint?
Lipschitz constrained networks are neural networks with bounded derivatives. They have many applications ranging from adversarial robustness to Wasserstein distance estimation. There are various ways to enforce such constraints.
What is Lipschitz method?
A method for testing diuretic activity in rats has been described by Lipschitz et al. ( 1943). The test is based. on water and sodium excretion in test animals and compared to rats treated with a high dose of urea. The “Lipschitz-value” is the quotient between excretion by test animals and excretion by the urea control …
What is Lipschitz stability?
DEFINITION 1.1 [ 51. The zero solution of (1.1) is said to be uniformly. Lipschitz stable if there exists M> 1 and 6 > 0 such that 1 x(t, t,, x0)1 < M I x0 I for 1 x0 1 < 6 and t b to > 0. The constant M is called the Lipschitz.
How do you determine if a function is Lipschitz?
Suppose that f is a real-valued function defined and difierentiable on an interval I ⊂ R. If f/ is bounded on I, then f is a Lipschitz function on I. for some c between x and y, and it follows that |f(y) − f(x)| ≤ M|y − x|. Thus (2) holds with C = M.
What is Lipschitz condition in differential equation?
In the theory of differential equations, Lipschitz continuity is the central condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem. A special type of Lipschitz continuity, called contraction, is used in the Banach fixed-point theorem.
Is a Lipschitz function continuous?
Any Lipschitz function is uniformly continuous. for all x, y ∈ E. The function f (x) = √x is uniformly continuous on [0,∞) but not Lipschitz.
Are Lipschitz functions uniformly continuous?
A function f : E → R is called a Lipschitz function if there exists a constant L > 0 such that |f (x) − f (y)| ≤ L|x − y| for all x,y ∈ E. Any Lipschitz function is uniformly continuous.
Is Lipschitz stronger than continuity?
The definition of Lipschitz continuity is also familiar: Definition 2 A function f is Lipschitz continuous if there exists a K < ∞ such that f(y) − f(x) ≤ Ky − x. It is easy to see (and well-known) that Lipschitz continuity is a stronger notion of continuity than uniform continuity.