PomeDefinition 21.11.30.D6A0CB1B8846 Let $F\in \mathrm{Conv}(N)$ and $n\in N$. An element $m\in M$ is a subgradient (in the sense of Alexandrov) of $F$ at $n$ if
F6F028287E9D
21.11.31
\begin{equation} F(n')\geq F(n)+\langle n'-n,m \rangle ,\quad \forall n'\in N. \end{equation}
The set of subgradients of $F$ at $n$ is denoted by $\nabla F(n)$.
More generally, for any subset $E\subseteq N$, we write
\[ \nabla F(E)=\bigcup _{n\in E}\nabla F(n). \]
Comments
Corrections, questions, and mathematical discussion are welcome. Sign in with GitHub to comment. Comments are public.