I'm working on programming models stemming from convex analysis ideas for various data-sets.
The functions I'm working with tend to be downwawrd facing cones, which is to say if you imagine for instance a function like $z = -\sqrt{x^2+y^2}$, this forms a cone that opens downward in the $-z$ direction.
Well, I'd like to conjecture that any concave map from $\mathbb R^n$ to $\mathbb R$ that is bounded above has a unique global maximum. Can anyone find a credible reference for this? Unfortunately google and wikipedia didn't quite yield the exact results I'm looking for.