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Re: [Help-gsl] conjugate gradient problem

From: James Bergstra
Subject: Re: [Help-gsl] conjugate gradient problem
Date: Sun, 29 Jan 2006 03:14:32 -0500
User-agent: Mutt/

> this 'temp1' returned is supposed to be printed by s->f in main(). 's' is 
> actually passed to 'gsl_multimin_fdfminimizer_iterate (s)'; in each iteration 
> But a different value is printed in main. To be precise its printing the 
> value of arr[0]* arr[1] & NOT arr[0]*arr[1]+ temp3.
> Now temp3 uses term[i] array, which is calculated like exp(-20*linear 
> constraint1) + exp(-20*linearconstraint2) + ..... + 
> exp(-20*linearconstraintN). in another function.

I have three ideas, of which perhaps none will be useful...

You are adding exp(-LARGENUMBER*??) several times, which might be very small
compared with arr[0]*arr[1] and cause a rounding error.

You are mis-understanding the role of s->f in main().  This variable stores
the current lowest value found in the codomain.  In the later stages of 
not every call to your function will reveal a new lowest point.

You are forgetting my_fdf().  Perhaps your printf statements are duplicated in
my_fdf, but you are accidentally returning the wrong value in my_fdf ?

> Now my another 2 problems are:
> 2> for this constrained case the output never prints the 'Minima Found'.

That's normal. Iterative minimization routines do not reliably converge in a
reasonnable time.  You can try other minimization routines too... each of them
works well sometimes.

> 3> After some 10 iterations the function value & variable values does not 
> change any more with iterations. & at the same time for each iteration it 
> enters into my_f(ie, the function where the function 'xy' is calculated). 
> Initially for each iteration it enters my_f only once (as is expected)
> but as th function & variable values stops changing it enters the my_f 
> function succesively more no. of times for each iteration. ... why should it 
> be like that ??

Good question.  I have almost no idea, but you could look at the references in
the manual, or even just google for conjugate-gradient.  The issue is
theoretical, and it's related to the algorithm.  It is not a bug in the library.

Good luck.

james bergstra

On Sun, Jan 29, 2006 at 12:39:18AM +0530, Debashree.Sen wrote:
> hi,
>     i am using GSL for doing multidimensional minimization of a non-linear 
> functions of dimensions ( max 20-30). I was trying to minimize a quadratic 
> function by employing exponential barrier method on it ( for non-linear 
> programming problem of operation research).
> The function to be minimised is 'xy'. this is how i have defined my function:
> /*This is the multidimensional quadratic function being minimised*/
> double my_f (const gsl_vector *v, void *params)
>      {
>       printf("\ninside my_f\n");
>            double *dp = (double *)params;
>             /*Variable declarations*/
>            double temp = 0;
>            double temp0 = 0, temp2 = 0;
>            double temp1 = 0, temp3 = 0;
>            int i=0, j=0, k;
>          /*Initialising the multi-dim array*/
>             for(;i<ndim;i++)
>                        arr[i] = gsl_vector_get(v, i);
>             for(i=0;i<num;i++)
>                       temp3+=exp(-LARGENUMBER*term[i]); // Largenumber can be 
> anything say 10-20--here                
>                                                              this is the 
> exponential barrier 
>             printf("temp= %lf",temp3);
>           temp1 = arr[0]*arr[1]+temp3;                  // a function of the 
> type , say , x*y
>             printf("func value: %lf", temp1); -------------> at this stage 
> value calculated is correct
>             return temp1;                    //The final function value
>       }

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