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

```

• Prev by Date: Re: Getting started with 3D cardioid
• Next by Date: FindMaximum doesn't converge
• Previous by thread: Re: i get an empty figure when exporting it, if I keep
• Next by thread: Re: Why is Newton's method failing to "find sufficient increase in function"?