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Topic: An optimization problem
Replies: 19   Last Post: Sep 14, 2013 9:44 AM

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 quasi Posts: 12,067 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

Date Subject Author
9/7/13 analyst41@hotmail.com
9/7/13 RGVickson@shaw.ca
9/7/13 quasi
9/7/13 RGVickson@shaw.ca
9/8/13 quasi
9/8/13 quasi
9/7/13 RGVickson@shaw.ca
9/7/13 William Elliot
9/8/13 quasi
9/8/13 Peter Percival
9/8/13 quasi
9/8/13 Peter Percival
9/8/13 quasi
9/8/13 Peter Percival
9/8/13 Timothy Murphy
9/9/13 AP
9/9/13 RGVickson@shaw.ca
9/11/13 analyst41@hotmail.com
9/12/13 RGVickson@shaw.ca
9/14/13 analyst41@hotmail.com