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Re: Keeping global parameters in an evaluated function

Hi Davide,

Looks like your guess about initial evaluation of the function is correct.
If you restrict your argument to be numeric, you get what you want:

ff[x_?NumericQ] := (x - c)^4
c = 1;
iterations = 1;
FindMinimum[ff[x], {x, 1001}, StepMonitor :> {c = c/2; iterations++}]
Print[{c // N, iterations}]

Out[88]= {1.0531*10^-30, {x -> 3.20345*10^-8}}

During evaluation of In[84]:= {5.16988*10^-26,85}


On Wed, Oct 20, 2010 at 1:10 AM, Davide Mancusi <d.mancusi at> wrote:

> Hello everyone,
> I have a function that depends on some variables and a parameter (say
> c). My goal is to find the global minimum of the function for a given
> value of the parameter, say c=0. However, the function has a lot of
> local minima for c=0, and is thus very difficult to hit the global
> one. For c=1, however, the function is much smoother, and the
> minimization algorithms work pretty well.
> What I'm trying to do is to change the value of the parameter
> continuously while Mathematica minimizes the function. By doing so I
> hope to trap the minimization algorithms close to the global minimum
> using the smooth version of the function, and then slowly let c go to
> 0.
> I have come up with the following toy model (I use NMinimize in the
> real problem, but that shouldn't be important):
>  f[x_] := (x - c)^4
>  c=1;
>  iterations=1;
>  FindMinimum[ f[x], {x, 1001}, StepMonitor :> {c = c/2; iterations+
> +} ]
>  Print[{c // N,iterations}]
> If I run this I get
>  {4.48416*10^-32, {x -> 1.}}
>  {1.45519*10^-11,37}
> The algorithm finds the minimum at x==1 while I would like it to find
> it close to 1.45519*10^-11.
> I think the problem lies in the fact that f[x] is evaluated only once,
> at the beginning of the minimization algorithm, and the global value
> of c gets substituted. Thus, even if I change c later, that doesn't
> affect the function being minimized.
> Can anyone suggest a way to update c from within the minimization
> routine?
> Thanks in advance,
> Davide

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