Re: Two successive FindMinimum -> Bug?

*To*: mathgroup at smc.vnet.net*Subject*: [mg74352] Re: Two successive FindMinimum -> Bug?*From*: Peter Pein <petsie at dordos.net>*Date*: Mon, 19 Mar 2007 02:09:09 -0500 (EST)*References*: <etik3j$j32$1@smc.vnet.net>

Dmitry Garanin schrieb: > Hi All, > > I am trying to solve a problem that requires application of FindMinimum (or similar rutines two times and it does not work. Here is a simplified example: > > > fxt[x_,t_]=(x^2-t)^2 (* Searching for a minimal t for which fxt turns to zero *) > tminx[x_]:=t/.FindMinimum[fxt[x,t],{t,1}][[2]] (* Finding the minimizing t for a given x *) > tminabs=FindMinimum[tminx[x],{x,1}] (* Minimizing this t with respect to x. The result should be tminabs=0 at x=0 *) > > The last command here does not work since, evidently tminx[x] (that is x^2 for us humans) is not treated as a regular function. > > Is there a bug here or I am doing something wrong?? > > Help is appreciated. > > > http://profiles.yahoo.com/dgaranin > Hi Dmitry, either define tmin as a function of numerical arguments: tmin[x_?NumericQ]:=... or (for simple functions fxt) tmin[x_]:= t /. ToRules[Reduce[D[fxt[x,t],t] == 0 && D[fxt[x,t], {t,2}] > 0, t]] hth, Peter