       complicated vector-valued function

• To: mathgroup at smc.vnet.net
• Subject: [mg45480] complicated vector-valued function
• From: "Johannes Ludsteck" <johannes.ludsteck at wiwi.uni-regensburg.de>
• Date: Sat, 10 Jan 2004 00:00:28 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```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]]},

Mathematica responds to this with the error message

NMinimize::bcons : The following constraints are not
valid:
{f[{\$1,\$2},SparseArray[<2>,{2,2}]==\$1,f[{\$1,\$2},SparseArr
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
NMinimize?

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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