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On Sun, 06 Jun 2004 19:24:42 -0700, 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.
Is the lim{d->INFINITY}(C1(d)) defined in the real numbers. If so let
C1(INFITIY) be the lim{d->INFINITY}(C1(d)). Clearly if C1(INFINITY)
exists then C1(INFINITY)+C2(1) must be less than C(d) for all d and thus
the minimum exists.
Based strictly on what you have given, I do not think it possible to
develop a finite time algorithm for finding a d that produces the minimum
C(d) value (if it exists).
Lance Lamboy
