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 > >