Is it true that every unbounded convex set in $R^n$ has a recession direction? I think there is a counterexample, because I have not assumed that the convex set is closed.
I have not been able to come up with a counterexample though. Does anyone know if this is true?
In a finite dimensional space, any unbounded convex has a recession direction, should it be closed or not.
That may not be the case for infinite dimensional spaces though.
See here for details.