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MathGroup Archive 2006

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Re: Points sampled by FindMinimum

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71175] Re: Points sampled by FindMinimum
  • From: "dimitris" <dimmechan at yahoo.com>
  • Date: Thu, 9 Nov 2006 03:41:15 -0500 (EST)
  • References: <eisfsu$mrp$1@smc.vnet.net>

See the following commands

FindMinimum[func[x], {x, 0.1}, EvaluationMonitor :> Print[x]]
0.1
0.1
0.10000000149011612
0.6
0.6
0.6000000089406967
0.9999999776482598
0.9999999776482598
0.9999999925494206
0.9999999925494208
0.9999999925494208
1.000000007450582

{1., {{a, {2, 28}} -> 0.9999999925494208}}

FindMinimum[func[x], {x, 0.1}, StepMonitor :> Print[x]]
0.6
0.9999999776482598
0.9999999925494208
{1., {{a, {2, 28}} -> 0.9999999925494208}}

After read carefully the reply of Andrzej Kozlowski to a similar query
of mine
regarding FindRoot which appeared here

http://groups.google.com/group/comp.soft-sys.math.mathematica/browse_thread/thread/7534c7180ecd7408/73d759a6749fb2bd?lnk=st&q=FindRoot+Step&rnum=1&hl=en#73d759a6749fb2bd

More specifiacally watch there he said that

"... In general EvaluationMonitor (and also Print statement I add) will
produce more
values than StepMonitor, because it records each time the specified
numerical
function is evaluated. Sometimes to make one step in an iterative
procedure you need to evaluate the function several times at
different points (the standard example is when you need to compute a
numerical derivative using finite differences) and all these
computations will be part of one step (so will not be recorded by
StepMonitor) but will be recored by EvaluationMonitor..."

Regards
Dimitris


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