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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 8, 2013 2:04 AM

Ray Vickson wrote:
>quasi wrote:
>> 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

>
>This formula is incorrect: it should be (as in my previous post)
>
> all x = [sqrt(n+1)-1]/n.

Yes, agreed.

I used Maple for the algebra, but didn't notice that I had a typo
in my input.

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