Re: Baffled by FindMinimum

*To*: mathgroup at smc.vnet.net*Subject*: [mg124903] Re: Baffled by FindMinimum*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Sat, 11 Feb 2012 06:38:59 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201202101055.FAA00702@smc.vnet.net>

>From the documentaion for FindMinimum: "FindMinimumfirst localizes the values of all variables, then evaluates f with the variables being symbolic, and then repeatedly evaluates the result numerically." Since you don't want ObjectiveFunction to try evaluating with a symbolic argument, restrict its definition to a vector of numeric arguments. In general, restrict the definition of any function to numeric arguments when the function uses numeric techniques. Clear[ObjectiveFunction] ObjectiveFunction[p : {__?NumericQ}] := (p[[3]] - 1)^2 + Norm[p] /; Length[p] > 2 p0 = {1, 2, 2, 1, 2}; FindMinimum[ObjectiveFunction[xx], {xx, {1, 2, 3, 2, 1, 2}}] {0.75, {xx -> {-5.48284*10^-9, -7.29576*10^-9, 0.5, -7.02789*10^-9, -5.48284*10^-9, -7.02789*10^-9}}} Bob Hanlon On Fri, Feb 10, 2012 at 5:55 AM, Sam Takoy <sam.takoy at yahoo.com> wrote: > Hi, > > Please take a look at this simple code. > > ObjectiveFunction[p_] := Module[{}, > Print["Why is this p: ", p]; > (p[[3]] - 1)^2 + Norm[p]] > p0 = {1, 2, 2, 1, 2}; > FindMinimum[ObjectiveFunction[xx], {xx, {1, 2, 3, 2, 1, 2}}] > > If you run it, you will find that ObjectiveFunction is called with the > argument "xx" rather than the numerical vector. How come? > Also, judging by the lack of the Print statement firing, > ObjectiveFunction is not called again. Yet, it eventually (after > complaining of understandable errors) produces the correct answer. > What's going on here? I would expect if to be called repeated in the > course of numerical minimization. I'm completely baffled by what's > going on here. > > Here's the output: > > During evaluation of In[377]:= Why is this p: xx > > During evaluation of In[377]:= Part::partd: Part specification xx[[3]] > is longer than depth of object. >> > > During evaluation of In[377]:= Part::partd: Part specification xx[[3]] > is longer than depth of object. >> > > Out[380]= {0.75, {xx -> {-5.48284*10^-9, -7.29576*10^-9, > 0.5, -7.02789*10^-9, -5.48284*10^-9, -7.02789*10^-9}}} > > Many thanks in advance, > > Sam

**References**:**Baffled by FindMinimum***From:*Sam Takoy <sam.takoy@yahoo.com>