A Note on Local Min-Max affine approximations of real-valued continuous convex functions in $\mathbb R^k$ with applications to computer vision

We present a method to find local Min-Max affine approximants of continuous convex functions $f:\Delta\subset \mathbb R^k\to \mathbb R$ on a simplex $\Delta$ in $\mathbb R^k$. Our method finds an optimal affine approximant for the given f. We apply our result to an application in computer vision.