Re: how to proof the existence of minimum value

From: Virgil (ITSnetNOTcom/virgil_at_COMCAST.com)
Date: 06/07/04 

Date: Sun, 06 Jun 2004 20:57:14 -0600

In article <9e847e5e.0406061824.7a7bde69@posting.google.com>,
 buaanupt@sina.com (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.

Since functions defined only for integer arguments cannot in any way
have derivatives, I can see that derivatives might be very difficult to
obtain.

What are the ranges of your functions? Can they have arbitrary real
values or are they restricted to, say, integer values, or even positive
integer values?

I suspect that if the values can be arbitrary reals, or even arbitrary
integers, subject only to the monotonicity requirements, that desired
the conclusion may be false.

Are C1 and C2 weakly or strictly monotone, or does it matter?

Relevant Pages

  • Re: how to proof the existence of minimum value
    ... buaanupt@sina.com (ZHANG Yan) wrote: ... have derivatives, I can see that derivatives might be very difficult to ... I suspect that if the values can be arbitrary reals, ... integers, subject only to the monotonicity requirements, that desired ...
    (sci.math)
  • Re: [edstat] how to proof the existence of minimum value
    ... The gateway between this list and the sci.stat.edu newsgroup will ... have derivatives, I can see that derivatives might be very difficult to ... I suspect that if the values can be arbitrary reals, ... integers, subject only to the monotonicity requirements, that desired ...
    (sci.stat.edu)