Re: Startingpoint and Initial region in Nminimize

• To: mathgroup at smc.vnet.net
• Subject: [mg101316] Re: [mg101180] Startingpoint and Initial region in Nminimize
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Wed, 1 Jul 2009 06:33:44 -0400 (EDT)
• References: <200906261049.GAA18120@smc.vnet.net>

```laianhngoc at yahoo.com wrote:
> Hi All,
>
> I have 2 problems :
>
> + I don't know if one can assign ONE Startingpoint when using Nminimize.
>
> Example:
>
> f[S_, T_] := S^2 + (T - 10)^2;
> NMinimize[f[S, T], {{S, 2, 2.000001}, {T, 4, 4.00001}},
> Method -> {"NelderMead", "InitialPoints" -> {{-2, 30}}}];
>
> As you see, here i have an Initial region: {{S, 2, 2.000001}, {T, 4, 4.00001}}. The
> "InitialPoints" serve only as a reference for the final result.
>
> Now, i want Nminimize to take Exactly one Starting point (that i give For example {2,4}, not one region). Is it possible??? Sory if the question was already asked.
>
> ++ In addition, i observe that the Nminimize's iterations strongly depend on that Initial region. (Not in this simple case but in what i'm doing). Meaning:
>
> We can have different result when the Initial region is larger (For example)
> {{S, 2, 4}, {T, 4, 6}}
> or smaller {{S, 2, 2.0000001}, {T, 4, 4.000001}}.
>
> I do not see why??? because i think that this is just a starting point and the Initial region
> can not influence the result of the optimization.
>
> If someone have experiences about that two questions?
>
> Thanks a lot and regard,
> Anh.

NMinimize chooses pseudorandom points in its starting region. Hence the
region specification will change those starting points, and thus can
have an effect on the final outcome both in terms of quality and speed.

Daniel Lichtblau
Wolfram Research

```

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