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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.

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