quasi
Posts:
11,740
Registered:
7/15/05


Re: An optimization problem
Posted:
Sep 7, 2013 4:06 PM


analyst41 wrote:
>consider f(x1,x2,...xn) = {1 + sum(xi)^2)} / {1 +sum{x(i)} > >0 <=xi <=1 for all i. > >The maximum function value of 1 occurs at either >all x's = 0 or all x's = 1. > >Can an explicit formula be given for the minimum?
Yes.
The minimum value is
((2n)*((n+1)sqrt(n^2+n)))/sqrt(n^2+n)
which occurs when all x's are equal to
(sqrt(n^2+n)  n)/n
quasi

