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

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Posts: 12,067
Registered: 7/15/05
Re: An optimization problem
Posted: Sep 8, 2013 3:36 AM
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William Elliot wrote:
> 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?

>Let g(x) = (1 + x^2)/(1 + x) and look for extreme values of g.

The function g is not applicable.

From the context, the OP intended

f(x_1, ..., x_n) = (1 + sum((x_i)^2))/(1 + sum(x_i))

whereas you interpreted it (incorrectly) as

f(x_1, ..., x_n) = (1 + (sum(x_i))^2))/(1 + sum(x_i))

Of the two possible interpretations above, only the first is
consistent with the OP's claim that for all n, the maximum
value of f is 1.


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