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MathGroup Archive 1995

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FindRoot solved

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg472] FindRoot solved
  • From: Chengri Ding <ding at gis.uiuc.edu>
  • Date: Tue, 14 Feb 1995 15:02:40 -0600

Thanks for the listed people who help to solve my problem I posted a couple days ago.

Michael Trott
Wolfram Research, Inc.

Fredrick I. Olness
Internet:   Olness at phyvms.physics.smu.edu (129.119.200.74)
            Olness at mail.physics.smu.edu

Thx you for your help. I, fortunately solved the problem by using FindRoot command rather than NSovle after reformuling and correting somepart. But I still can
not use FindMinimum to get the same solution. I hope you can help me figure out
what is wrong. 

Ojective function is:
 
 -(k/E^(0.01*t)) + 0.6425702811245005*t - 0.0963855421686749*t^2 + 
   0.004819277108433735*t^3 + (3.375333333333331*10^7 + 
      5.001999999999999*10^6*k + 247050.*k^2 + 4066.666666666667*k^3 - 
      5533.333333333352*t - 820.000000000003*k*t - 40.50000000000017*k^2*t - 
      0.6666666666666691*k^3*t + 830.000000000002*t^2 + 
      123.0000000000003*k*t^2 + 6.075000000000017*k^2*t^2 + 
      0.1000000000000002*k^3*t^2 - 41.50000000000001*t^3 - 
      6.150000000000002*k*t^3 - 0.3037500000000002*k^2*t^3 - 
      0.005000000000000001*k^3*t^3)/
    (8611.25 + 1260.5625*k + 61.50000000000001*k^2 + 1.*k^3)
 
two first derivative function is
 
1:
 
  (1.818989403545856*10^-12*E^(0.01*t) + 86.1125*k - 10.*E^(0.01*t)*k + 
     12.605625*k^2 - 0.981927710843394*E^(0.01*t)*k^2 + 
     0.6150000000000001*k^3 - 0.02409638554216864*E^(0.01*t)*k^3 + 
     0.01*k^4 + 3.000000000000085*E^(0.01*t)*k*t + 
     0.2945783132530213*E^(0.01*t)*k^2*t + 
     0.007228915662650688*E^(0.01*t)*k^3*t + 
     1.4210854715202*10^-14*E^(0.01*t)*t^2 - 
     0.2250000000000014*E^(0.01*t)*k*t^2 - 
     0.02209337349397633*E^(0.01*t)*k^2*t^2 - 
     0.0005421686746987959*E^(0.01*t)*k^3*t^2)/
   (E^(0.01*t)*(8611.25 + 1260.5625*k + 61.50000000000001*k^2 + 1.*k^3))
 
2: 
 (-(7.415362656250001*10^7) + 5.252862500000154*10^8*E^(0.01*t) - 
     2.171003765625*10^7*k + 1.031586250000038*10^8*E^(0.01*t)*k - 
     2.64820156640625*10^6*k^2 + 7.596215625000001*10^6*E^(0.01*t)*k^2 - 
     172271.6875*k^3 + 248575.0000000149*E^(0.01*t)*k^3 - 6303.375*k^4 + 
     3050.*E^(0.01*t)*k^4 - 123.*k^5 + 
     1.818989403545856*10^-12*E^(0.01*t)*k^5 - 1.*k^6 - 
     86112.5000000028*E^(0.01*t)*t - 16911.25000000047*E^(0.01*t)*k*t - 
     1245.281250000058*E^(0.01*t)*k^2*t - 
     40.75000000000183*E^(0.01*t)*k^3*t - 
     0.5000000000000285*E^(0.01*t)*k^4*t - 
     4.440892098500627*10^-16*E^(0.01*t)*k^5*t + 
     12916.87500000035*E^(0.01*t)*t^2 + 2536.687500000058*E^(0.01*t)*k*t^2 + 
     186.7921875000065*E^(0.01*t)*k^2*t^2 + 
     6.112499999999728*E^(0.01*t)*k^3*t^2 + 
     0.07499999999999929*E^(0.01*t)*k^4*t^2 - 
     645.8437500000074*E^(0.01*t)*t^3 - 126.834375000004*E^(0.01*t)*k*t^3 - 
     9.33960937500024*E^(0.01*t)*k^2*t^3 - 
     0.3056250000000134*E^(0.01*t)*k^3*t^3 - 
     0.00374999999999992*E^(0.01*t)*k^4*t^3)/
   (E^(0.01*t)*(8611.25 + 1260.5625*k + 61.50000000000001*k^2 + 1.*k^3)^2)
 
and then I used FindRoot[{equ1==0,equ2==0},{t,50},{k,150}]
got solution:
 
{t -> 35.6386, k -> 44.2428}
 
But I cannot get solution by  FindMinimum[test3[t,k],{t,35},{k,44}]
The message is: FindMinimum::fmlim: The minimum could not be bracketed in 30 iterations.
 
Appreciate for your any further help.
 
chengri Ding
University of Illinois at Urbana-Champaign
 


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