  A closed subset $M$ of a Banach space $E$ is \ep, i.e., can be represented
locally as the epigraph of a Lipschitz function, if and only if it is the level
set of some locally Lipschitz function $f: E\to \R$, wich Clarke's generalized
gradient does not contain 0 at points in the boundary of $M$, i.e., such that:
M=\{x \mid f(x)\leq 0\}, 0\not \in \partial f(x) {if} x\in \bd M. This extends
the characterization previously known in finite dimension and answers to a
standing open question

Optimization and Control