* Proposition of a better convergion criterion in multimin
@ 2002-08-21 2:41 Philippe Huber
2002-08-26 13:12 ` Brian Gough
0 siblings, 1 reply; 2+ messages in thread
From: Philippe Huber @ 2002-08-21 2:41 UTC (permalink / raw)
To: gsl-discuss
Hi all,
I found that the stopping criterion proposed in
gsl_multimin_test_gradient suffers from scale problems. Typically, if
you have variables of magnitude 1.0e0 and a function of magnitude 1.0e5,
it can be impossible to minimize the norm of the gradient under 1.0e-2.
Dennis and Schnabel in "Numerical Methods for Unconstrained Optimization
and Nonlinear Equations", p.160 propose another criterion:
relgrad = gradfi * xi / f,
where gradfi is the ith component of the gradient and xi the ith
variable. The criterion is ||relgrad||inf < epsabs, with ||.||inf is the
infinite norm: ||x||inf=max(|xi|).
Here is a proposition of a new routine called gsl_multimin_test_relgrad:
int
gsl_multimin_test_relgrad (const gsl_vector *g, const gsl_vector *x,
double f, double epsabs)
{
int i;
double relgrad;
if (epsabs < 0.0)
{
GSL_ERROR ("absolute tolerance is negative", GSL_EBADTOL);
}
relgrad=fabs(gsl_vector_get(g,0)*gsl_vector_get(x,0)/f);
for(i=1;i<g->size;i++)
relgrad=gsl_max(relgrad,fabs(gsl_vector_get(g,i)*gsl_vector_get(x,i)/f))
;
if (relgrad < epsabs)
{
return GSL_SUCCESS;
}
return GSL_CONTINUE;
}
Take care
Phil
^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: Proposition of a better convergion criterion in multimin
2002-08-21 2:41 Proposition of a better convergion criterion in multimin Philippe Huber
@ 2002-08-26 13:12 ` Brian Gough
0 siblings, 0 replies; 2+ messages in thread
From: Brian Gough @ 2002-08-26 13:12 UTC (permalink / raw)
To: Philippe Huber; +Cc: gsl-discuss
Philippe Huber writes:
> I found that the stopping criterion proposed in
> gsl_multimin_test_gradient suffers from scale problems. Typically,
> if you have variables of magnitude 1.0e0 and a function of
> magnitude 1.0e5, it can be impossible to minimize the norm of the
> gradient under 1.0e-2. Dennis and Schnabel in "Numerical Methods
> for Unconstrained Optimization and Nonlinear Equations", p.160
> propose another criterion: relgrad = gradfi * xi / f, where gradfi
> is the ith component of the gradient and xi the ith variable. The
> criterion is ||relgrad||inf < epsabs, with ||.||inf is the infinite
> norm: ||x||inf=max(|xi|). Here is a proposition of a new routine
> called gsl_multimin_test_relgrad:
How about scaling the components of g? This would be invariant under
x->x+constant, f->f+constant which seems like a useful property.
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