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RE: NMinimize

  • To: mathgroup at smc.vnet.net
  • Subject: [mg81763] RE: [mg81740] NMinimize
  • From: "David Annetts" <davidannetts at aapt.net.au>
  • Date: Wed, 3 Oct 2007 02:27:19 -0400 (EDT)
  • References: <200710020947.FAA28904@smc.vnet.net>

Hi Raj, 

> Could somebody tell me if there is a better way to do this in
> Mathematica:
> data = Flatten@Import["moistureAtDepth1.dat"];
> data = data[[20000 ;; 30000]];
> ti = Import["times.dat"];
> func[x_, Di_, De_, t_, t1_, t2_] :=
>    (Erfc[x/Sqrt[2400 Di (t - t1)]] -
>    Erfc[x/Sqrt[2400 Di (t - t2)]] +
>    Erf[x/Sqrt[2400 De (t - t2) ]])
> parameters = {Di,De};
> NMinimize[ {Plus@@Table[ (data[[i-20000]] -
>       Plus @@ ((func[15.2, Di, De, i, First@#, Last@#] &) /@
>          Select[ti, i - 2880 <= #[[2]] <= i-1 
> &]))^2,{i,22881,25000}], 
> 10^-8<=Di<=10^-1,10^-8<=De<=10^-1},parameters]
> 
> I am interested in Optimizing  the NMinimize line.

Firstly, are you sure of your model?  The model you've given simplifies to 

	func[x_, Di_, De_, t_, t1_, t2_] := Erf[x/Sqrt[2400 De (t - t2) ]])

and Di is superfluous.

I would try to use FindMinimum[] rather that NMinimize[] as a first try.
Because this function finds local rather than global minima, it's much
quicker.  Depending on your data, this may be adequate.

Next, I would try NMinimize from the local minimum.  If that's not good
enough, there are many options for NMinimize that given better answers than
the default parameters.  Start with 

	Method -> {NelderMead, PostProcess -> KKT}

There's a tutorial at tutorial/MonitoringAndSelectingAlgorithms that you
should try after the one at tutorial/NumericalOptimization

Regards,

Dave.



  • References:
    • NMinimize
      • From: Raj <rajanikanth@gmail.com>
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