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MathGroup Archive 1995

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Re: Help !!!!

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg471] Re: [mg459] Help !!!!
  • From: withoff (David Withoff)
  • Date: Tue, 14 Feb 1995 13:07:36 -0600

> Dear Mathgroup,
> 
> I do some optimization practice using FindMinimum command. The Objective 
> function is :
> 
>  -k + 0.004*t*(93633.3333333333 + 529.9999999999999*t + t^2) + 
>    (0.005000000000000001*(1.566333333333333*10^7*k - 93633.3333333333*k*t - 
>         529.9999999999999*k*t^2 - 1.*k*t^3))/(0.75 + 1.*k)
> 
> But I could not get the solution for it. t and k are variables.
> the message I got is :
> 
> FindMinimum::fmlim: The minimum could not be bracketed in 30 iterations.
> 
> 
> The arguement is:  FindMinimum[test3[t,k],{t,50,80},{k,2,5}]
> 
> I hope someone can help me out. Very appreciate.
> 
> Chengri Ding
> Univeristy of Illinois at Urbana-Champaign

Since the global minimum of this function is -Infinity, it is important
to give good starting values to prevent the search algorithm from
searching forever in an infinitely negative part of the function.

By looking at plots of this function, it is not obvious that there
is a local minimum near {t,50,80} and {k,2,5}.

Possible minima will occur where

    D[test3[t, k], t] == 0
    D[test3[t, k], k] == 0

The following result

    In[5]:= Factor[D[Rationalize[test3[t, k]], t]]

                               2
            (3 - k) (530 + 3 t)
    Out[5]= --------------------
               750 (3 + 4 k)

indicates that finite minima can occur only for k == 3 or t == -530/3.
Unless I made a mistake somewhere, further analysis along these lines
shows that test[t, k] does not have any finite minima.

Dave Withoff
Research and Development
Wolfram Research


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