Re: Keeping global parameters in an evaluated function

*To*: mathgroup at smc.vnet.net*Subject*: [mg113271] Re: Keeping global parameters in an evaluated function*From*: Leonid Shifrin <lshifr at gmail.com>*Date*: Thu, 21 Oct 2010 07:03:23 -0400 (EDT)

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: In[84]:= Clear[ff]; 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} Regards, Leonid On Wed, Oct 20, 2010 at 1:10 AM, Davide Mancusi <d.mancusi at ulg.ac.be> 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 > >