Re: Points sampled by FindMinimum

• To: mathgroup at smc.vnet.net
• Subject: [mg71221] Re: Points sampled by FindMinimum
• From: "Andrew Moylan" <andrew.j.moylan at gmail.com>
• Date: Fri, 10 Nov 2006 06:38:56 -0500 (EST)
• References: <eisfsu\$mrp\$1@smc.vnet.net><eiut0d\$h42\$1@smc.vnet.net>

```Thanks for your responses. I see now that Mathematica is evaluating the
function at three nearby points as part of its finite-difference
approximation to the derivative.

Cheers,
Andrew

On Nov 9, 8:39 pm, "dimitris" <dimmec... at yahoo.com> wrote:
> 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
>
>
> 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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