I’m not trying to be a smartass about the word hull; I’m just curious to know if there is a good mathematical reason why the shape of the boundary you mention in the post would necessarily be convex.
I’m sorry, I’m not following you. The hull is convex by definition, no matter where the points are.
Thinking about it though, the appropriate figure to consider isn’t the convex hull, but the set of points which are not dominated by any other points. That can produce a concave figure, but it’s still true to say that when you switch between them, you have to lose on one axis to gain on another, again by definition.
I’m not trying to be a smartass about the word hull; I’m just curious to know if there is a good mathematical reason why the shape of the boundary you mention in the post would necessarily be convex.
I’m sorry, I’m not following you. The hull is convex by definition, no matter where the points are.
Thinking about it though, the appropriate figure to consider isn’t the convex hull, but the set of points which are not dominated by any other points. That can produce a concave figure, but it’s still true to say that when you switch between them, you have to lose on one axis to gain on another, again by definition.
That answers my question.