Any example of known strong convexity constant?

Question

A continuously differentiable function $f(x)$ is strongly convex on $\mathbb{R}^{n}$ if there exists a positive constant $\mu$ such that for any $x, y \ \in \mathbb{R}^{n}$, \begin{align} f(y)\geq f(x) + \langle \nabla f(x), y-x\rangle + \frac{1}{2}\mu \|y-x\|^2 \end{align} I'm curious about the strong convexity constant $\mu$. I heard that for some limited cases, it is known.

Could anyone tell me what kind of functions have a known value for $\mu$? For example, is it known for a quadratic function? I searched on Google but I haven't found any useful source.

Answer 1

For example, if $f(x) = \|x\|^2$, then $\nabla f(x) = 2 x$, and it's easy to show that your inequality becomes an equality if $\mu = 2$.