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Why is Newton's method failing to "find sufficient increase in function"?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112044] Why is Newton's method failing to "find sufficient increase in function"?
  • From: Yaroslav Bulatov <yaroslavvb at gmail.com>
  • Date: Thu, 26 Aug 2010 06:49:21 -0400 (EDT)

I'm getting FindMaximum::lstol warning in the code below...why? How
can I get rid of it?

For this particular function I can fix it by changing Method to
Automatic, but this breaks optimization for other functions in my
optimization task where Newton's method works fine.

o = 1/5 Log[E^(-(h/Sqrt[3]))/(
     2 E^(-(h/Sqrt[3])) + 2 E^(h/Sqrt[3]) +
      E^(-(h/Sqrt[3]) - Sqrt[2] j) + E^(h/Sqrt[3] - Sqrt[2] j) +
      E^(-Sqrt[3] h + Sqrt[2] j) + E^(Sqrt[3] h + Sqrt[2] j))] +
   1/5 Log[E^(h/Sqrt[3])/(
     2 E^(-(h/Sqrt[3])) + 2 E^(h/Sqrt[3]) +
      E^(-(h/Sqrt[3]) - Sqrt[2] j) + E^(h/Sqrt[3] - Sqrt[2] j) +
      E^(-Sqrt[3] h + Sqrt[2] j) + E^(Sqrt[3] h + Sqrt[2] j))] +
   1/10 Log[E^(-(h/Sqrt[3]) - Sqrt[2] j)/(
     2 E^(-(h/Sqrt[3])) + 2 E^(h/Sqrt[3]) +
      E^(-(h/Sqrt[3]) - Sqrt[2] j) + E^(h/Sqrt[3] - Sqrt[2] j) +
      E^(-Sqrt[3] h + Sqrt[2] j) + E^(Sqrt[3] h + Sqrt[2] j))] +
   3/10 Log[E^(h/Sqrt[3] - Sqrt[2] j)/(
     2 E^(-(h/Sqrt[3])) + 2 E^(h/Sqrt[3]) +
      E^(-(h/Sqrt[3]) - Sqrt[2] j) + E^(h/Sqrt[3] - Sqrt[2] j) +
      E^(-Sqrt[3] h + Sqrt[2] j) + E^(Sqrt[3] h + Sqrt[2] j))] +
   1/10 Log[E^(-Sqrt[3] h + Sqrt[2] j)/(
     2 E^(-(h/Sqrt[3])) + 2 E^(h/Sqrt[3]) +
      E^(-(h/Sqrt[3]) - Sqrt[2] j) + E^(h/Sqrt[3] - Sqrt[2] j) +
      E^(-Sqrt[3] h + Sqrt[2] j) + E^(Sqrt[3] h + Sqrt[2] j))] +
   1/10 Log[E^(Sqrt[3] h + Sqrt[2] j)/(
     2 E^(-(h/Sqrt[3])) + 2 E^(h/Sqrt[3]) +
      E^(-(h/Sqrt[3]) - Sqrt[2] j) + E^(h/Sqrt[3] - Sqrt[2] j) +
      E^(-Sqrt[3] h + Sqrt[2] j) + E^(Sqrt[3] h + Sqrt[2] j))];
ContourPlot @@ {o, {j, -1, 1}, {h, -1, 1}}
FindMaximum @@ {o, {{j, -0.008983550852535105`}, {h,
    0.06931364191023386`}}, Method -> "Newton"}


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