Suppose a multivariable function f:R^n->R is concave and sufficiently smooth. We have: ∥f(x)−f(x0)∥<=M∥x−x0∥ for some positive constant M.

4enevi 2022-10-23 Answered
Suppose a multivariable function f : R n R is concave and sufficiently smooth. We have:
f ( x ) f ( x 0 ) M x x 0 for some positive constant M.
If the f is univariate, we know that M is the absolute value of the slope of the tangent line at x 0 . But what is it for multivariable case, is there a special name in math given to it?
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Answers (1)

zupa1z
Answered 2022-10-24 Author has 20 answers
This is the definition of Lipschitz continuity. M is called the Lipschitz constant of f.
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