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Black box optimization

  • To: mathgroup at
  • Subject: [mg126282] Black box optimization
  • From: "McHale, Paul" <Paul.McHale at>
  • Date: Sat, 28 Apr 2012 05:29:17 -0400 (EDT)
  • Delivered-to:

Is there any black box optimization of user defined non-polynomial functions in Mathematica?  I.e.

I want to minimize fm[x] between 0.010 and 0.060.  The goal is to fit the data with mx+b.   This requires two points.  The first point in the data has to be zero or first element shown below.  The other single point must allow a fit with minimum error between the original data points and the new data points generated from an mx+b approximation.

(* Use mMinFit to select Y value for selected point *)
mMinFit=Fit[Select[InData, #[[1]] > 0.01&],{1,x},x];
(* Generate fit between new fit between first point and new test point *)
mFit=Fit[{First@InData,{mPt,mMinFit /. x->mPt}},{1,x},x];
(* subtract real data from points generated by new curve  *)
mError=Total@Table[Abs@(m[[2]]-mFit /. x ->m[[1]]),{m,InData}]

Calling fm[0.01] calculates the fit using {{0.`,0.3457378`},{0.01,InterpValue} as the two points mx+b must pass through.  It then returns the Abs[] of
 the difference between the original points (InData) and the interpolated points based on original x values.  This is intended to be the error function.  Minimizing fm[x] should give the best possible choice of x to calibrate with.

I can always fall back to:

First@Sort[m,#1[[2]] < #2[[2]]&]

Out:= {0.04474,2.13522}

Here is a decent graph of the issue:

ListPlot[Table[fm[i], {i, 0.010, 0.060, 0.001}], Joined -> True]

I thought I found a better way in Mathematica before...

Paul McHale  |  Electrical Engineer, Energetics Systems  |  Excelitas Technologies Corp.

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Paul.McHale at

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