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Problem behavior with FindMaximum

• To: mathgroup at smc.vnet.net
• Subject: [mg59671] Problem behavior with FindMaximum
• From: "James H. Steiger" <jsteiger at bellsouth.net>
• Date: Wed, 17 Aug 2005 04:00:24 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hello all:

I wonder if you could give me some advice about behavior of FindMaximum[]
that I cannot seem to decipher.

There is a broad class of problems in statistics that involves finding the
maximum
of a function of several parameters, all but one (call it "a") of which are
*nuisance parameters*.
The function is evaluated at any value of "a" by maximizing it w.r.t. all
the nuisance parameters.

A simple example (constructed just for Mathgroup -- the actual
functions I work with are messier)  should make this clear.


myFunc1[a_, b_] := 1/((a - 16)^2 + 1) - (a - b)^2
myFunc2[a_] := FindMaximum[myFunc1[a, b], {b, 0}][[1]]

FindMaximum returns a list, the first element of which is the maximized
value of the function,
the second of which is a replacement rule specifying the value of b at which
the maximum occurs.

As you can quickly verify, myFunc2 is well behaved, and you can plot myFunc2
without incident.

Plot[myFunc2[a],{a,14,18}] produces a nice plot with no error messages

Here is where the problem arises. Suppose you want to use FindMaximum[] to
obtain the maximum of myFunc2 which clearly occurs at 
a=16.

If you input the command

FindMaximum[myFunc2[x],{x,14}]

you obtain a pair of error messages (can anyone tell me how to copy these in
Mathematica as text?)

-----------------

FindMaximum::nnum: The function value 1/((1+<<1>>)^2) - (0.+a)^2 is not a
number at {b}={0.}

FindMaximum::nnum: The function value 0.2 - (14. -b)^2 is not a number at
{a}={14.}

-----------------

Is there some problem of "scope" of these variables that I am not aware of?
Or is there some bug in FindMaximum[]?
Is there a fix?

Thanks to all,

Jim


James H. Steiger, Professor and Director
Quantitative Methods and Evaluation
Dept. of Psychology and Human Development
Vanderbilt University
Peabody College #512
Nashville, TN, 37203

Phone: 615-322-7060
email: james.h.steiger at vanderbilt.edu 

• Follow-Ups:
  • Re: Problem behavior with FindMaximum
    • From: "benshimo@bgumail.bgu.ac.il" <bsyehuda@gmail.com>
  • Re: Problem behavior with FindMaximum
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>