minlbfgs_numdiff and the likelihood function [solved]

andmon · **Joined:** Tue May 28, 2013 8:10 pm **Posts:** 2

Hi all,

I would like to find the minimum of a likelihood function using minlbfgs_numdiff (numerical differentiation). Clearly, my function depends on an array of data (vvv[]).
I do not understand why it ends up in an infinite loop. Here is the driver I have created.
Have you got any suggestions, please?
Best,
A

Code:

void function1_func(const real_1d_array &x, double &func, void *ptr)
{
    
        int i;
   double a=0;
   double s = 0;
   double e=0;
   double err=0;
   for(i = 0; i<10; i++)
   {      
     e= vvv[i]-x[0];
     a= -0.5*log(2*PI)-0.5*(log(x[1])+(e*e)/x[1]);
     s=s+a;

   }
   func= (s);
    
}

Sergey.Bochkanov · **Joined:** Fri May 07, 2010 7:06 am **Posts:** 927

The most likely reason is that your function is not defined at x[1]<=0 and is not bounded from below at x=0. So, it does not have clear defined global minimum. So, either:
* L-BFGS algorithm accidentally steps into x[1]<0 and fails (eternal loop is a possible failure scenario)
* L-BFGS algorithm eternally explores sequence of increasingly better x[], with x[1]->0.

I recommend you to use BLEIC algorithm with boundary constraint x[1]>=eps where eps is some small number.

andmon · **Joined:** Tue May 28, 2013 8:10 pm **Posts:** 2

Thanks for your reply. Actually I fixed the code simply changing "func(s)" to "func(-s)" and everything works.

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