NMinimize

• To: mathgroup at smc.vnet.net
• Subject: [mg68362] NMinimize
• From: "jour" <jour at ccr.jussieu.fr>
• Date: Wed, 2 Aug 2006 05:24:30 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi

I am new in this usenet group, I am a chemist in Paris working on
Molecular Magnetism and I  try to optimize my experimental data to
theoretical models

I sent two hours ago my first subject to this group about
NonlinearRegress

here is the theoretical function (Debye model for heat capacity)

deb[teta_,n_,t]:= 9 n (t/teta)^3 Nintegrate[(x^4
Exp[x])/(1+Exp[x])^2,{x,0,t/teta}]

I can Table this function without problem

Table[{t, deb2[100, 3, t]}, {t, 1, 200, 5}]

but when I try to use this function in NonlinearRegress

fut = NonlinearRegress[dat,
deb2[teta, n, t],
{t}, {{teta, {10., 50.}, 0., 1000.}, {n, {1, 3}, 1, 70}}]

I get an error message

NIntegrate::"nlim"  t/teta is not a valid limit of integration

Actually I have the same problem with NMinimize

nmin = NMinimize[{Sum[(deb2[teta,n, dat[[i,1]]] - dat[[i, 2]])^2, {i,
Length[dat]}], 1 = n = 80 && 1
= teta = 300 }, {n, teta}, Method ->
"DifferentialEvolution"]

I get  the following message error
NIntegrate::"nlim"  x = 6.6778/tetais not a valid limit of integration

There is a tiny improvement because Mathematica  gives a numerical
value to t. But in both approaches Mathematica does not give any
numerical value to the parameters

I get the same kind of problem if the theoretical function is obtained
by numerical diagonalization of matrices where MATHEMATICA try to
diagonalize the matrix without numerical value

Is there any way to solve these kind of problems ?

I would be very grateful if somebody could help me on this problem

best regards

Yves

```

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