[R] optim seems to be finding a local minimum

Dimitri Liakhovitski dimitri.liakhovitski at gmail.com
Mon Nov 14 23:26:49 CET 2011

Just to provide some closure:

I ended up dividing the IV by its max so that the input vector (IV) is
now between zero and one. I still used optim:
myopt <- optim(fn=myfunc, par=c(1,1), method="L-BFGS-B", lower=c(0,0))
I was able to get great fit, in 3 cases out of 10 I've beaten Excel
Solver, but in 7 cases I lost to Excel - but again, by really tiny
margins (generally less than 1% of Excel's fit value).

Thank you everybody!

On Fri, Nov 11, 2011 at 10:28 AM, John C Nash <nashjc at uottawa.ca> wrote:
> Some tips:
> 1) Excel did not, as far as I can determine, find a solution. No point seems to satisfy
> the KKT conditions (there is a function kktc in optfntools on R-forge project optimizer.
> It is called by optimx).
> 2) Scaling of the input vector is a good idea given the seeming wide range of values. That
> is, assuming this can be done. If the function depends on the relative values in the input
> vector rather than magnitude, this may explain the trouble with your function. That is, if
> the function depends on the relative change in the input vector and not its scale, then
> optimizers will have a lot of trouble if the scale factor for this vector is implicitly
> one of the optimization parameters.
> 3) If you can get the gradient function you will almost certainly be able to do better,
> especially in finding whether you have a minimum i.e., null gradient, positive definite
> Hessian. When you have gradient function, kktc uses Jacobian(gradient) to get the Hessian,
> avoiding one level of digit cancellation.
> JN
> On 11/11/2011 10:20 AM, Dimitri Liakhovitski wrote:
>> Thank you very much to everyone who replied!
>> As I mentioned - I am not a mathematician, so sorry for stupid
>> comments/questions.
>> I intuitively understand what you mean by scaling. While the solution
>> space for the first parameter (.alpha) is relatively compact (probably
>> between 0 and 2), the second one (.beta) is "all over the place" -
>> because it is a function of IV (input vector). And that's, probably,
>> my main challenge - that I am trying to write a routine for different
>> possible IVs that I might be facing (they may be in hundreds, in
>> thousands, in millions). Should I be rescaling the IV somehow (e.g.,
>> by dividing it by its max) - or should I do something with the
>> parameter .beta inside my function?
>> So far, I've written a loop over many different starting points for
>> both parameters. Then, I take the betas around the best solution so
>> far, split it into smaller steps for beta (as starting points) and
>> optimize again for those starting points. What disappoints me is that
>> even when I found a decent solution (the minimized value of 336) it
>> was still worse than the Solver solution!
>> And I am trying to prove to everyone here that we should do R, not Excel :-)
>> Thanks again for your help, guys!
>> Dimitri
>> On Fri, Nov 11, 2011 at 9:10 AM, John C Nash <nashjc at uottawa.ca> wrote:
>>> I won't requote all the other msgs, but the latest (and possibly a bit glitchy) version of
>>> optimx on R-forge
>>> 1) finds that some methods wander into domains where the user function fails try() (new
>>> optimx runs try() around all function calls). This includes L-BFGS-B
>>> 2) reports that the scaling is such that you really might not expect to get a good solution
>>> then
>>> 3) Actually gets a better result than the
>>>> xlf<-myfunc(c(0.888452533990788,94812732.0897449))
>>>> xlf
>>> [1] 334.607
>>> with Kelley's variant of Nelder Mead (from dfoptim package), with
>>>> myoptx
>>>  method                        par       fvalues fns  grs itns conv  KKT1
>>> 4 LBFGSB                     NA, NA 8.988466e+307  NA NULL NULL 9999    NA
>>> 2 Rvmmin           0.1, 200186870.6      25593.83  20    1 NULL    0 FALSE
>>> 3 bobyqa 6.987875e-01, 2.001869e+08      1933.229  44   NA NULL    0 FALSE
>>> 1   nmkb 8.897590e-01, 9.470163e+07      334.1901 204   NA NULL    0 FALSE
>>>   KKT2 xtimes  meths
>>> 4    NA   0.01 LBFGSB
>>> 2 FALSE   0.11 Rvmmin
>>> 3 FALSE   0.24 bobyqa
>>> 1 FALSE   1.08   nmkb
>>> But do note the terrible scaling. Hardly surprising that this function does not work. I'll
>>> have to delve deeper to see what the scaling setup should be because of the nature of the
>>> function setup involving some of the data. (optimx includes parscale on all methods).
>>> However, original poster DID include code, so it was easy to do a quick check. Good for him.
>>> JN
>>>> ## Comparing this solution to Excel Solver solution:
>>>> myfunc(c(0.888452533990788,94812732.0897449))
>>>> -- Dimitri Liakhovitski marketfusionanalytics.com
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Dimitri Liakhovitski

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