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[Help-gsl] BFGS iteration does not make any progress
From: |
Hannes Bretschneider |
Subject: |
[Help-gsl] BFGS iteration does not make any progress |
Date: |
Wed, 13 Apr 2011 21:23:03 +0200 |
So I have a problem with the multidimensional minimization procedures
in the GSL (the one I'm trying to use is
gsl_multimin_fdfminimizer_vector_bfgs2, but the others produce the
same problem). I have defined my target function and its gradient and
I can start the iteration, but the algorithm always stays at the same
point.
Now, I thought I would have a math error in my function or gradient
somewhere. However, for a specific set of data I know the optimum and
plugging in those values produces a gradient that is 0 everywhere.
If I start the iteration at the optimum, the algorithm correctly stops
and reports success, but if I disturb the starting vector only
minimally, the iteration runs forever and never finds the optimum.
I also reimplemented the function and gradient in R. I checked that
the C version and the R version produce the same output for the same
input, which they do. Using the BFGS algorithm in R, the optimum is
found in just a few iterations.
I initialize the algorithm with
const gsl_multimin_fdfminimizer_type *T;
gsl_multimin_fdfminimizer *s;
gsl_multimin_function_fdf lindsey_func;
const gsl_vector * p[] = {x, y};
lindsey_func.n = J;
lindsey_func.f = lindsey_loglik;
lindsey_func.df = lindsey_gradient;
lindsey_func.fdf = lindsey_gf;
lindsey_func.params = p;
T = gsl_multimin_fdfminimizer_vector_bfgs2;
s = gsl_multimin_fdfminimizer_alloc(T, J);
gsl_multimin_fdfminimizer_set(s, &lindsey_func, beta0, .001, 1e-4);
and the iteration looks like this:
do
{
iter++;
status = gsl_multimin_fdfminimizer_iterate(s);
printf("%d\n", status);
if (status)
break;
status = gsl_multimin_test_gradient(s->gradient, 1e-3);
if (status == GSL_SUCCESS)
{
printf("Minimum found at: ");
printf("[");
for (j = 0; j < J; j++)
{
printf("%.5f, ", gsl_vector_get(s->x, j));
}
printf("]\n");
}
} while (status == GSL_CONTINUE && iter < iter_max);
The only parameter that I can tweak are the initial step size and the
accuracy of the line minimization ingsl_multimin_fdfminimizer_set
(gsl_multimin_fdfminimizer * s, gsl_multimin_function_fdf * fdf, const
gsl_vector * x, double step_size, double tol). Trying different values
there has a small effect (sometimes the algorithm moves a little bit),
but I can't find any values that actually make the algorithm move
around.
Thanks for any suggestions!
--Hannes
- [Help-gsl] BFGS iteration does not make any progress,
Hannes Bretschneider <=