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I'm doing a non-linear fit on some data. The calculation residual is low, but I prefer to minimize another objective function such as: 

Mean((|exp - calc)/exp|)*100

When I try to to minimize with that objective function, the results are not encouraging.

I'll try to explain better: if I calculate the fit and then the objective function, I get 0.957233; if I minimize the objective function directly, I get 0.991929. I expected it to go vice-versa.

In my real problem, I've got 4000 data points and the difference is not acceptable. 

Clear["Global`*"]
data = {
  {0.1067`, 0.535903658`, 0.272`, 39.90165169`},
  {0.1059`, 0.526916509`, 0.272`, 39.90165169`}, 
  {0.1017`, 0.544890806`, 0.272`, 39.90165169`}, 
  {0.1055`, 0.512537072`, 0.272`, 39.90165169`},
  {0.1035`, 0.526916509`, 0.272`, 39.90165169`},
  {0.1132`, 0.455019322`, 0.272`, 39.90165169`}, 
  {0.1108`, 0.472993619`, 0.272`, 39.90165169`}, 
  {0.1084`, 0.490967916`, 0.272`, 39.90165169`}, 
  {0.1059`, 0.508942213`, 0.272`, 39.90165169`}
};
exp = data[[All, 1]];
trexp = data[[All, 2]];
ccfexp = data[[All, 3]];
radiusexp = data[[All, 4]];
fit = NonlinearModelFit[data[[All, {2, 3, 4, 1}]], 
  a*(1 + ccf)^b + (100 + grr)^c/(1 + tr)^d,
  {{a, 0.1}, {b, 0.1}, {c, 0.1}, {d, 0.1}}, 
  {ccf, tr, grr}];
f[ccf_, grr_, tr_, a_, b_, c_, d_] = 
  a*(1 + ccf)^b + (100 + grr)^c/(1 + tr)^d;
desigma = 
  100*Mean[Map[
    Abs[(#[[1]] - f[#[[3]], #[[4]], #[[2]], a, b, c, d])/#[[1]]] &, 
    data]];
(* NMinimize*)
m1 = NMinimize[desigma, {a, b, c, d}][[1]]
(* NonlinearModelFit *)
m2 = Mean[Abs[fit["FitResiduals"]/fit["Response"]]]*100
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1  
I get 0.7409745686 as the result for NMinimize... – Sjoerd C. de Vries Mar 8 at 23:29
@SjoerdC.deVries With some particular Method? If I copy and paste my original code in a blank notebook I've got the same results of the question... {0.991929, {a -> -0.00601452, b -> 1.50111, c -> -0.327449, d -> 1.32326}} – Mary Mar 9 at 8:19
I just copied your code. Mathematica 9.0.1 Win7-64. Have you tried completely restarted Mathematica? – Sjoerd C. de Vries Mar 9 at 9:20
I, too, tried to evaluate your code. It has many problems with variable naming resulting in both undefined and unused variables. – m_goldberg Mar 9 at 14:45

closed as too localized by Oleksandr R., m_goldberg, Sjoerd C. de Vries, rm -rf♦ Mar 24 at 15:09

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