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MathGroup Archive 2004

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Re: nonlinear programming with differential-algebraic constraints (2)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52136] Re: nonlinear programming with differential-algebraic constraints (2)
  • From: Joerg Schaber <schaber at molgen.mpg.de>
  • Date: Fri, 12 Nov 2004 02:13:49 -0500 (EST)
  • References: <cmsok4$b72$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Thanks for your replies.
Indeed, the problem was that I have to define a function or module to be 
called in NMinimize that gets evaluated every time with the new 
parameter. I solved it now by defining a module, but the solutions using 
  functions are also very elegant, I think.

Thanks,
joerg

Joerg Schaber wrote:
> I made a little example to illustrate the problem:
> 
> I want to fit a model which is stated as a system of differenttial 
> equations to some data.
> 
> (* curve to be fitted *)
> f[t_]:=Exp[-0.1*t]+Random[Real,{0,0.1}];
> data={#,Evaluate[f[#]]}&/@Table[t,{t,0,10,1}];
> 
> ListPlot[data,PlotStyle\[Rule]{RGBColor[0,0.2,0.8],PointSize[0.02]}];
> 
> (* the parameter 0.1 is to be found *)
> (* the model as a differential equations *)
> model:=NDSolve[{y'[t]==-a*y[t],y[0]==1}/.a->0.05,y,{t,0,10}];
> 
> (* minimizing sum of squares *)
> NMinimize[{squares=Plus@@Table[(Table[{#,y[t]/.Evaluate[model][[1]]/.t->#}&/@
> 		Table[t,{t, 0, 10, 1}]][[i, 2]]-data[[i,2]])^2,
> 		{i, Length[data]}], a > 0}, a,
> 		Method -> {"DifferentialEvolution"},
> 		StepMonitor :> Print[squares, a],
> 		WorkingPrecision -> 8]
> 
> 
> The main problem seems to be that the differential equation does not get 
> evaluated in each step but only once.
> 
> So if anybody could make this example work that would be great.
> 
> best,
> 
> joerg
> 


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