On totally Fenchel unstable functions in finite dimensional spaces
We give an answer to the Problem 11.6 posed by Stephen Simons in his book "From Hahn-Banach to Monotonicity": Do there exist a nonzero finite dimensional Banach space and a pair of extended real-valued, proper and convex functions which is totally Fenchel unstable? The answer is negative.
conjugate function fenchel duality recession cone