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[EMAIL PROTECTED] (ZHANG Yan) wrote:
>
>Suppose that d is positive integer, i.e. d=1,2,3...
>
>A function is defined as follows.
>
>C(d)=C1(d)+C2(d)
>
>Now, I have to proof that there exists an optimal d, see d_{op},
>leading to minimum C(d). And also I have to find an algorithm to find
>d_{op}.
>
>I am able to proof that C1(d) is decreasing function of d, and C2(d)
>is increasing function of d. Note that no closed-form expression for
>C1(d) or C2(d), or even has closed-form, its first and second
>derivative is extremely difficult to obtain.
Try
C1(d)=10/d^2
C2(d)=-1/d^2
C1(d) is a decreasing function and C2(d) is an increasing function of
d for positive integers d.
Then
C(d)=9/d^2
This C(d) is strictly decreasing, and has no minimum value.
You will have to extract more information from the original problem
if you want to show that C(d) has a minimum.
For example, if C2(d) is an unbounded function, and C1(d) is bounded,
then you can easily show that C(d) will have a minimum on the positive
integers.
Without knowing more about the original problem, no one on this group
will be in a position to help...
--
Brian Borchers [EMAIL PROTECTED]
Department of Mathematics http://www.nmt.edu/~borchers/
New Mexico Tech Phone: 505-835-5813
Socorro, NM 87801 FAX: 505-835-5366
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