Area constraint in 2-d roots?

Area constraint in 2-d roots?

[Peter S. Christopher]

Hi there,
	I'm inquiring about the gsl_multiroot_fsolver_iterate function.
Specifically I'm interested in constraining the allowable solutions that
the algorithm searches to a small area.

I'm using the gsl_multiroot_fsolver_hybrids algorithm. I am passing a
function that looks something like this

int zeroBmu(const gsl_vector *x, void *params, gsl_vector * f){
	...
	...
  m0 = gsl_vector_get(x,0);
  mA = gsl_vector_get(x,1);
	...
	...	
  return GSL_SUCCESS;
}


My problem is that I need to bracket m0 and mA; specifically these
parameters must be > 0.0 and < 1.0. The solution I'm using is something
like 

int zeroBmu(const gsl_vector *x, void *params, gsl_vector * f){
        ...
        ...
  /*be sure that x0,x1 are both > 0.0*/
  gsl_vector_set((gsl_vector *)x, 0, fabs(gsl_vector_get(x,0)));
  gsl_vector_set((gsl_vector *)x, 1, fabs(gsl_vector_get(x,1)));

  m0 = gsl_vector_get(x,0);
  mA = gsl_vector_get(x,1);
  if( m0 >= 1.0)
    {
	/*do something that forces m0 to be smaller then 1.0. */
        gsl_vector_set((gsl_vector *)x,0,m0);
    }
  if(mA >= 1.0)
    {
	/*ext.*/
    }
        ...
        ...
	...
  return GSL_SUCCESS;
} 

MY 2 QUESTIONS:
	1) Will this provide the appropriate constraint.
	2) Is there a more "elegant" way to do this. Maybe one that is
built into the solvers. Maybe something that doesn't force me to break the
"const gsl_vector *" of x with a cast.


Thanks for any help,

Pete Christopher

Re: Area constraint in 2-d roots?

[Brian Gough]

Peter S. Christopher writes:
 > Hi there,
 > 	I'm inquiring about the gsl_multiroot_fsolver_iterate function.
 > Specifically I'm interested in constraining the allowable solutions that
 > the algorithm searches to a small area.

GSL doesn't have any routines for constrained minimization.

You can use a penalty function to safely discourage the minimizer from
going outside the desired region.  Modification of const arguments is
definitely not recommended.

regards
Brian Gough