# More general multidimensional minimization in Rb-GSL?

**URL:** <https://www.ruby-forum.com/t/more-general-multidimensional-minimization-in-rb-gsl/109353>\
**Category:** Ruby\
**Created:** [July 13, 2007, 5:50pm UTC](https://www.ruby-forum.com/t/more-general-multidimensional-minimization-in-rb-gsl/109353 "2007-07-13T17:50:56Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![Axel\_E](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/a/7c8e57/32.png) [@Axel\_E](https://www.ruby-forum.com/u/Axel_E)\
**Post date:** [July 13, 2007, 5:50pm UTC](https://www.ruby-forum.com/t/more-general-multidimensional-minimization-in-rb-gsl/109353/1 "2007-07-13T17:50:56Z")

</div>

Dear all,

in Ruby-Gsl’s multidimensional minimization, the FMinimizer function  
requires an equal number of variables and parameters, as  
illustrated in the example

include GSL::MultiMin

my\_f = Proc.new { |v, params|  
x = v[0]; y = v[1]  
p0 = params[0]; p1 = params[1]  
10.0\*(x - p0)_(x - p0) + 20.0_(y - p1)\*(y - p1) + 30.0  
}

my\_df = Proc.new { |v, params, df|  
x = v[0]; y = v[1]  
p0 = params[0]; p1 = params[1]  
df[0] = 20.0\*(x-p0)  
df[1] = 40.0\*(y-p1)  
}

my\_func = Function\_fdf.alloc(my\_f, my\_df, 2)  
my\_func.set\_params([1.0, 2.0]) # parameters

Can this be generalized somehow … without tinkering with the  
C code ?

More precisely, I’d like to do some minimization of the values  
of a vector under some constraints, like:

m\*(target-vector)= minimal,

where m is a matrix,  
all entries of vectors target and vector are whole numbers,  
but differ in a prescribed number of entries .

(Pseudo-)inverting m is not really an option, as can it be quite big (  
several thousand lines / rows ).  
I’ve tried to implement the constraints in a Proc involving m and  
target, called on vector, but can’t get it to work with the Ruby-GSL  
minimization  
FMinimizer.

Any ideas?

Thank you very much,

Axel

---

<div class="post-metadata">

**Author:** ![Axel\_E](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/a/7c8e57/32.png) [@Axel\_E](https://www.ruby-forum.com/u/Axel_E)\
**Post date:** [July 14, 2007, 5:50am UTC](https://www.ruby-forum.com/t/more-general-multidimensional-minimization-in-rb-gsl/109353/2 "2007-07-14T05:50:24Z")

</div>

Axel E. wrote:

> p0 = params[0]; p1 = params[1]  
> my\_func = Function\_fdf.alloc(my\_f, my\_df, 2)  
> where m is a matrix,  
> Thank you very much,
> 
> Axel

I’m not familiar with the minimization algorithms in GSL, but if you  
don’t mind using R, most of the constrained and unconstrained algorithms  
are in an R package called “optim”:

optim package:stats R Documentation

General-purpose Optimization

Description:

```
 General-purpose optimization based on Nelder-Mead, quasi-Newton
 and conjugate-gradient algorithms. It includes an option for
 box-constrained optimization and simulated annealing.

```

There is an R-Ruby interface called, I think, RSRuby, and I think it’s  
available as a gem. I personally like Nelder-Mead for small problems. It  
converges very slowly but it seldom gets trapped in false local minima,  
is robust, will handle constraints easily and works where fancier things  
don’t. For large problems, it’s probably too slow to be practical.

The “optim” code itself is written in C and is available in the package  
source if you want to interface it directly to Ruby. Or you could just  
pick up Nash’s book and implement the algorithm directly.

```
 Nash, J. C. (1990) _Compact Numerical Methods for Computers.
 Linear Algebra and Function Minimisation._ Adam Hilger.
```