Re: Problem behavior with FindMaximum
- To: mathgroup at smc.vnet.net
- Subject: [mg59698] Re: [mg59671] Problem behavior with FindMaximum
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Thu, 18 Aug 2005 00:16:31 -0400 (EDT)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
myFunc1[a_,b_]:=1/((a-16)^2+1)-(a-b)^2;
myFunc2[a_?NumericQ]:=FindMaximum[myFunc1[a,b],{b,0}][[1]];
Note that the definition of myFunc2 is restricted to numeric values of its
argument
Solve[{
D[myFunc1[a,b],a]==0,
D[myFunc1[a,b],b]==0},
{a,b}]
{{b -> 16, a -> 16}}
FindMaximum[myFunc1[a,b],{{a,0},{b,0}}]
{1., {a -> 15.999999999999945, b -> 15.999999999999947}}
FindMaximum[myFunc2[x],{x,14}]
{0.9999999999999858, {x -> 15.99999988089842}}
Bob Hanlon
>
> From: "James H. Steiger" <jsteiger at bellsouth.net>
To: mathgroup at smc.vnet.net
> Date: 2005/08/17 Wed AM 04:00:24 EDT
> Subject: [mg59698] [mg59671] Problem behavior with FindMaximum
>
> 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
>
>