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.
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.
>
> Could you plz give some suggestions to proceed? Many thanks in
> advance.
The details that you've given are not sufficient to obtain your result.
One technique to locate such a minimum is to find a value of d that
causes (C1 + C2)' to be zero, that is, that forces C1' to be equal to
-C2'. However, it's pretty much impossible to see whether this is
a feasible approach, since you have decided not to let us in on the secret.
Dale
