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MathGroup Archive 2004

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Evaluation of numeric Functions in NMinimize

  • To: mathgroup at
  • Subject: [mg45478] Evaluation of numeric Functions in NMinimize
  • From: "Johannes Ludsteck" <johannes.ludsteck at>
  • Date: Fri, 9 Jan 2004 05:20:49 -0500 (EST)
  • Organization: Universitaet Regensburg
  • Sender: owner-wri-mathgroup at

Dear MathGroup members, 
I try to find the fixed point of a complicated vector-valued  
function involving large SparseArray expressions with NMinimize  
by minimizing a constant and including the fixed point problem  
as a set of constraints. 
(The trivial example below is created only in order to mimic the  
structure of the problem.) 

dim = 2; 
i = SparseArray[{i_, i_} -> 1., {dim, dim}]; 
z = Table[Unique[], {dim}]; 
start = Table[1., {dim}]; 
f[x_ /; VectorQ[x, NumericQ], i_] := x.i.x; 

NMinimize[{1, Sequence @@ Thread[z == f[z, i]]}, 
  Thread[{z, 0.5 start, 1.5 start}]] 

Mathematica responds to this with the error message 

NMinimize::bcons : The following constraints are not valid: 

Apparently, Mathematica does not evaluate f because of the  
condition x_/: VectorQ[x,NumericQ] in the definition of f. 
This condition is, however necessary (not in the example here,  
but in my real world application). 

Is there any way to urge Mathematica to evaluate f in NMinimize? 

I am quite shure that everything else in my code is OK, because  
it works with FindRoot. 

Best regards, 
	Johannes Ludsteck 

Johannes Ludsteck
Economics Department
University of Regensburg
Universitaetsstrasse 31
93053 Regensburg
Phone +49/0941/943-2741

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