There are Many Totally Convex Functions
Dan Butnariu, Simeon Reich, Alexander J. Zaslavski · Journal of convex analysis · 2006
Let K K be a convex subset of a normed linear space and let R^1 R 1 denote the real line. We show that there are many (in the sense of Baire category) strictly convex and totally convex functions f \colon K \to R^1 f : K → R 1 . It is known that the existence of such functions is crucial in numerous optimization algorithms.