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Using NMinimize to solve a system of equations

  • To: mathgroup at
  • Subject: [mg52972] Using NMinimize to solve a system of equations
  • From: "OKULA Danielle" <DOKULA at>
  • Date: Sat, 18 Dec 2004 03:59:51 -0500 (EST)
  • Sender: owner-wri-mathgroup at


I am trying to use NMinimize to solve a system of equations, but I have been plagued with OverFlow, Underflow and division by zero problems when I change my F, L and WorkingPrecision.  Is there any other method in Mathematica to get reliable solutions to my equations ?

f[F_, L_] := E^(-((F/a)^b/b)) - E^(-((L/a)^b/b)); 
NMinimize[{0, f[100, 1000]/f[1000, 2613.01757776] == 
     2768.91499137093/3351.95653836949 && 
    f[1000, 2613.01757776]/f[5000, 10000] == 
     3351.95653836949/1680 && 
    f[100, 1000]/f[5000, 10000] == 2768.91499137093/
      1680 && 0. < b < 1. && 10^(-16) < a < 10^11}, 
  {a, b}, WorkingPrecision -> 20, MaxIterations -> 5000, 
  AccuracyGoal -> 15, PrecisionGoal -> 15, 
  EvaluationMonitor :> Print[{a, b}]]

Thank you in advance,


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