# Calculation/Estimate of Lipschitz Constant for Strictly Convex Function

I have a strictly convex function

$f(\bf{x}) = \dfrac{1}{2}\bf{x'Ax + b'x}$

where $\bf{f} : \mathbb{R^n} \rightarrow \mathbb{R}$

and I was wondering how I can find/estimate the Lipschitz constant. I'm in an introductory nonlinear optimization course and I've never seen this before.

I did some searching and found various things like

$|| f(x) - f(y) || \leq L ||x-y||$ where $L$ is the Lipschitz constant

but I'm unsure how to actually use this on a specific, randomly generated function. I'm trying to implement the Nesterov optimal first order method if that helps.

Thanks!

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Is $f$ even lipschitz continuous? Let $A=I$ and $b=0$, then $f(x) = \frac{||x||^2}{2}$. Since the derivative of $x^2$ is unbounded on $\mathbb{R}$, I'd say $f(x)$ is not lipschitz continuous. It's locally lipschitz continuous, though, because the derivative of $x^2$ is bounded on every bounded set. – fgp Oct 16 '12 at 18:18