Using NMinimize to solve a system of equations

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

```Hi,

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 ?

In[43]:=
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}]]

Danielle

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