golden section search fails when minimum is on the edge of the interval

[Peter Rockett]

I am using GS search embedded inside another optimiser and occasionally 
the minimum of the function ends up on the edge of the interval, i.e. 
when searching over [a..b], the minimum is at exactly at either a or b. 
In this situation, the GSL routine fails with: "gsl: fsolver.c:126: 
ERROR: endpoints do not enclose a minimum". As far as I understand, GS 
search should cope with this situation, hence its specification in terms 
of finding a minimum in the closed (cf open) interval [a..b]. Therefore, 
I suspect this is a bug.

An MWE (effectively copied from the manual example but with a modified 
fn1 fucntion)  is attached.

FWIW: The brent solver fails with exactly the same error.


#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#include <gsl/gsl_errno.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_min.h>

double fn1(double x, void* params)
    {
    (void)(params); /* avoid unused parameter warning */
    return x;
    }

int main(void)
    {
    int status;
    int iter = 0, max_iter = 100;
    const gsl_min_fminimizer_type* T;
    gsl_min_fminimizer* s;

    double m = 0.5;
    double a = 0.0, b = 1.0;

    gsl_function F;
    F.function = &fn1;
    F.params = 0;
    T = gsl_min_fminimizer_goldensection;
    s = gsl_min_fminimizer_alloc(T);
    gsl_min_fminimizer_set(s, &F, m, a, b);
    printf("using %s method\n", gsl_min_fminimizer_name(s));
    printf("%5s [%9s, %9s] %9s %10s %9s\n", "iter", "lower", "upper", 
"min", "err");
    printf("%5d [%.7f , %.7f ] %.7f %.7f \n", iter, a, b, m, b - a);
    do
        {
        iter++;
        status = gsl_min_fminimizer_iterate(s);
        m = gsl_min_fminimizer_x_minimum(s);
        a = gsl_min_fminimizer_x_lower(s);
        b = gsl_min_fminimizer_x_upper(s);
        status = gsl_min_test_interval(a, b, 0.001, 0.0);
        if(status == GSL_SUCCESS)
            printf("Converged:\n");
        printf("%5d [%.7f , %.7f ] " "%.7f %+.7f \n", iter, a, b, m, b 
- a);
        }
    while(status == GSL_CONTINUE && iter < max_iter);

    gsl_min_fminimizer_free(s);

    return status;
    }