Re: [Help-gsl] Multidimensional minimization problem

[Rhys Ulerich]

Oops.  This time with the list CCed...

> I am running multidimensional minimization along the lines of the examples
> in chapter 36.9 of the manual. gsl_multimin_fminimizers seem to converge to
> the correct answers when dimension of the problem is low.
>
> e.g. setting VECLEN=10 (see code below) delivers:
>
>>converged to minimum at
>> 6606 f() =   0.000 size = 0.000
>
> However when I raise dimension e.g. to 18 the algorithms seem to get stuck
> into clearly wrong answer
>
>>999999 f() = 237.603 size = 0.000

I agree that it seems gsl_multimin_fminimizer_nmsimplex probably
should get this one right, but I'm afraid I don't know the guts of the
algorithm.  Printing more precision I see it get stuck in some sort of
a hiccup a la
  74915 f() =   238.8119354938235404 size = 0.0000004931914997
  74916 f() =   238.8119354938235404 size = 0.0000004941216761
  74917 f() =   238.8119354938235404 size = 0.0000004931914997
  74918 f() =   238.8119354938235404 size = 0.0000004941216761
  74919 f() =   238.8119354938235404 size = 0.0000004931914997
  74920 f() =   238.8119354938235404 size = 0.0000004941216761
  74921 f() =   238.8119354938235404 size = 0.0000004931914997
  74922 f() =   238.8119354938235404 size = 0.0000004941216761
  74923 f() =   238.8119354938235404 size = 0.0000004931914997
where you can see the iterates oscillating.  Changing the STEPSIZE
sumply changes where the algorithm gets stuck:
  49020 f() =   117.9245273558944547 size = 0.0000002658725425
  49021 f() =   117.9245273558944547 size = 0.0000002659099457
  49022 f() =   117.9245273558944547 size = 0.0000002658725425
  49023 f() =   117.9245273558944547 size = 0.0000002659099457
  49024 f() =   117.9245273558944547 size = 0.0000002658725425
  49025 f() =   117.9245273558944547 size = 0.0000002659099457
  49026 f() =   117.9245273558944547 size = 0.0000002658725425
  49027 f() =   117.9245273558944547 size = 0.0000002659099457
  49028 f() =   117.9245273558944547 size = 0.0000002658725425
  49029 f() =   117.9245273558944547 size = 0.0000002659099457
  49030 f() =   117.9245273558944547 size = 0.0000002658725425

I do see gsl_multimin_fminimizer_nmsimplex2 getting the VECLEN 18
problem to f() = 0.50421136 given TOLERANCE 2e-15 in about 1.5M
iterations.  I haven't checked if it similarly gets stuck with
oscillating iterates.

I'd be interested to hear if you track down the source of these
oscillating iterates.

To be fair, you're cheating when you say it's a simple problem.  :)
You intuitively know the derivatives but neither
gsl_multimin_fminimizer_nmsimplex nor
gsl_multimin_fminimizer_nmsimplex2 does.

Hope that helps,
Rhys