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complicated vector-valued function

  • To: mathgroup at
  • Subject: [mg45480] complicated vector-valued function
  • From: "Johannes Ludsteck" <johannes.ludsteck at>
  • Date: Sat, 10 Jan 2004 00:00:28 -0500 (EST)
  • 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 
ay[<2>, {2,2}]==$2,f[{$1,$2},SparseArray[<2>,{2,2}]==$3}. 

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 

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

Best regards, 
	Johannes Ludsteck  
Johannes Ludsteck
Institut fuer Volkswirtschaftslehre
Lehrstuhl Prof. Dr. Moeller
Universitaet Regensburg
Universitaetsstrasse 31
93053 Regensburg
Tel +49/0941/943-2741

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