37.6 Stopping Criteria

A minimization procedure should stop when one of the following conditions is true:

• A minimum has been found to within the user-specified precision.
• A user-specified maximum number of iterations has been reached.
• An error has occurred.

The handling of these conditions is under user control. The functions below allow the user to test the precision of the current result.

Function: int gsl_multimin_test_gradient (const gsl_vector * g, double epsabs)

This function tests the norm of the gradient g against the absolute tolerance epsabs. The gradient of a multidimensional function goes to zero at a minimum. The test returns GSL_SUCCESS if the following condition is achieved,

|g| < epsabs

and returns GSL_CONTINUE otherwise. A suitable choice of epsabs can be made from the desired accuracy in the function for small variations in x. The relationship between these quantities is given by \delta f = g \delta x.

Function: int gsl_multimin_test_size (const double size, double epsabs)

This function tests the minimizer specific characteristic size (if applicable to the used minimizer) against absolute tolerance epsabs. The test returns GSL_SUCCESS if the size is smaller than tolerance, otherwise GSL_CONTINUE is returned.