Re: convex function through finite points with minimal area

[Jeff Barnett]

Markus wrote, On 4/16/2013 1:06 PM:

> Hello everyone,
>
> last week I found a question during my seminar work and couldn't solve
> it. I'm wondering if anybody else wants to work on this since the
> question is pretty easy but a solution turns out to be (at least) not
> as easy as the question. So,
>
> Given function values y_i for finite x_i's in the interval (0,1) such
> that the frequency polygon can be convex. What is the convex function
> with the least area connecting the points (0,0) and the (x_i,y_i)'s?
>
> I had different ideas, the most important (and somewhat only useful) is
> that I can look in the class of piecewise linear functions for the
> 'solution'. Furthermore, I should have n pieces and the pieces are
> somehow centered at (x_i,y_i).
>
> All the best,
> Markus

What about the convex hull of the (x_i, y_i) and (0,0)? Perhaps I don't
understand what you really want.

[
Moderator Note: I believe Markus wants the least area below the graph,
but the convex hull will have the greatest area.
]