Re: NMinimize Bug in Mathematica 7.0?

*To*: mathgroup at smc.vnet.net*Subject*: [mg96320] Re: NMinimize Bug in Mathematica 7.0?*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Wed, 11 Feb 2009 05:23:31 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <200902091033.FAA12301@smc.vnet.net> <gmrltf$9h0$1@smc.vnet.net>

In article <gmrltf$9h0$1 at smc.vnet.net>, "Jaccard Florian" <Florian.Jaccard at he-arc.ch> wrote: > I would avoid to use numerical methods without looking at a graphic. > As you can see: > Plot[x - 3*x^2 + x^4,{x, -2, 2}] > > Both answers are correct, they give approximations of local minimums. > You can ask for a minimal and maximal bound for the local minimums like = > this : > > In[8]:= NMinimize[x - 3*x^2 + x^4,{x, -2, -1}] > > Out[8]= {-3.513905038934789, > {x -> -1.3008395739047898}} > > In[9]:= NMinimize[x - 3*x^2 + x^4,{x, 0.5, 1.5}] > > Out[9]= {-1.0702301817761541, > {x -> 1.1309011226299863}} > > If you want the absolute minimum, use a non-numeric method : > > In[11]:= N[Minimize[x - 3*x^2 + x^4, x]] > > Out[11]= {-3.5139050389347894,{x -> -1.3008395659415772}} NMinimize[] is designed to find *global* minima. The text cell just above the input cell of the first example on the online documentation for NMinimize[] reads: "Find the global minimum of an unconstrained problem" Then the following example is given, In[1]:= NMinimize[x^4 - 3 x^2 + x, x] Out[1]= {-1.07023, {x -> 1.1309}} And the result is clearly wrong since it is not a *global* minimum contrary to what is claimed in this very same documentation. One should never forget that the Mathematica documentation centre is a "live" environment, that is, one can re-evaluate the cells (great feature), which also means that when the documentation for a given release is generated anew, therefore the new bugs in Mathematica functions are also carried on in the documentation itself. Regards, --Jean-Marc

**References**:**NMinimize Bug in Mathematica 7.0?***From:*appris@att.net