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Re: Black box optimization

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126358] Re: Black box optimization
  • From: "McHale, Paul" <Paul.McHale at excelitas.com>
  • Date: Thu, 3 May 2012 22:22:47 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hi,

I found an answer to the question.

If you have a generic function that returns an error magnitude driving by parameter when calling...

f[x_]:=Module[{error},
-- Some data computation --;
error= -- Some error generator function --;
error
]

NMinimize[] will use derivatives to find the minimum.  This is great unless you have numeric data and algorithms.  To motivate numerical methods:

NMinimize[fm[x], x]

Switch the definition to:

f[x_?NumericQ]:=Module[{error},
-- Some data computation --;
error= -- Some error generator function --;
error
]

This will force use of numerical algorithms.  There may be a better way, but this one works very well.  I'm not sure why NMinimize[] doesn't seem to detect this correctly without the NumericQ addition. 

Thanks,
Paul


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

Phone:   +1 937.865.3004   |   Fax:  +1 937.865.5170   |   Mobile:   +1 937.371.2828
1100 Vanguard Blvd, Miamisburg, Ohio 45342-0312 USA
Paul.McHale at Excelitas.com
www.excelitas.com



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-----Original Message-----
From: McHale, Paul
Sent: Friday, April 27, 2012 9:24 AM
To: mathgroup at smc.vnet.net
Subject: [mg126358] Black box optimization

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.

fm[mPt_]:=Module[{mMinFit,mFit,mError,x,InData},
InData={{0.`,0.3457378`},{0.005005030108147661`,0.5947282`},{0.010167934319260488`,1.110245`},{0.015746789471210974`,1.753068`},{0.019877754878728275`,2.26061`},{0.025058168807019193`,2.891833`},{0.029851036834650214`,3.470055`},{0.03486106617079409`,4.088596`},{0.04009652061250109`,4.721034`},{0.04501992441075972`,5.31037`},{0.049993105670535644`,5.912859`},{0.054948450286312706`,6.513352`},{0.06007028590992394`,7.144364`}};
(* 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:

m=Table[{i,fm[i]},{i,0.010,0.060,0.00001}];
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.

Phone:   +1 937.865.3004   |   Fax:  +1 937.865.5170   |   Mobile:   +1 937.371.2828
1100 Vanguard Blvd, Miamisburg, Ohio 45342-0312 USA Paul.McHale at Excelitas.com www.excelitas.com



Please consider the environment before printing this e-mail.
This email message and any attachments are confidential and proprietary to Excelitas Technologies Corp. If you are not the intended recipient of this message, please inform the sender by replying to this email or sending a message to the sender and destroy the message and any attachments.
Thank you




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