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# Proposition of a better convergion criterion in multimin

• From: Philippe Huber <huberph at infomaniak dot ch>
• To: gsl-discuss at sources dot redhat dot com
• Date: Wed, 21 Aug 2002 11:41:19 +0200
• Subject: Proposition of a better convergion criterion in multimin

```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;

if (epsabs < 0.0)
{
GSL_ERROR ("absolute tolerance is negative", GSL_EBADTOL);
}
for(i=1;i<g->size;i++)

;

if (relgrad < epsabs)
{
return GSL_SUCCESS;
}

return GSL_CONTINUE;
}

Take care

Phil

```

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