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

 Messages: [ Previous | Next ]
 RGVickson@shaw.ca Posts: 1,677 Registered: 12/1/07
Re: An optimization problem
Posted: Sep 7, 2013 6:21 PM

On Saturday, September 7, 2013 12:49:51 PM UTC-7, quasi wrote:
> analyst41 wrote:
>
>
>

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

This formula is incorrect: it should be (as in my previous post)
all x = [sqrt(n+1)-1]/n.
This can be verified numerically using an optimization package such as LINGO or the Maple Optimization facility or the EXCEL Solver, etc.

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