I'm dealing with this problem.
Let $\Lambda(y) := \max_{x\in P}c^\top x + y^\top x$
where $P$ is a polytope (a compact polyhedral set).
I need to characterize the subgradients of $\Lambda(\tilde{y})$ for fixed $\tilde{y}$.
Is there a way to write $\Lambda(\tilde{y})$ in terms of the extreme points of $P$ ?