The meaning of a symbol in Monotone operator

Question

I'm learning monotone operator these days and can't figure out the meaning of the symbol.

If you know the symbol please tell me.

Thanks for your time!

$$\nabla^2 f(x) \succeq mI$$

Answer 1

To add to Tom Ariel's answer, $A \succeq B$ means $A-B$ is a positive semidefinite operator. In matrix analysis literature, it is also called Löwner partial ordering on the symmetric matrices $\mathbb{S}^n$.

$A \succeq B$ if and only if $A-B\in \mathbb{S}^n_{+}$, where $\mathbb{S}^n_{+}$ is the positive semidefinite cone.