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Startingpoint and Initial region in Nminimize

  • To: mathgroup at smc.vnet.net
  • Subject: [mg101180] Startingpoint and Initial region in Nminimize
  • From: laianhngoc at yahoo.com
  • Date: Fri, 26 Jun 2009 06:49:08 -0400 (EDT)
  • Reply-to: laianhngoc at yahoo.com

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.      


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