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Topic: convex function through finite points with minimal area
Replies: 1   Last Post: Apr 17, 2013 9:15 AM

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Posts: 2
From: Istanbul
Registered: 4/16/13
convex function through finite points with minimal area
Posted: Apr 16, 2013 3:06 PM
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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,

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