[SOLVED] Scipy optimize SLSQP: How is the 'ftol' parameter used?

Scipy optimize SLSQP: How is the 'ftol' parameter used?

I am wondering how the 'ftol' paramater in scipy.optimize.minimize(method='SLSQP') is used. In the documentation it just says, that it is the precision goal for the value of f, which could mean different things. I know there is a paper where the original algorithm is explained; you can find it here:

http://yetanothermathprogrammingconsultant.blogspot.com/2022/02/slsqp-original-paper.html

However, I am not able to find the stopping criterion herein. Scipy provides a wrapper to the algorithm explained in that paper, which, I believe, is written in FORTRAN and not easy to read.

Thank you in advance!

Solution

Looking at the code in https://github.com/scipy/scipy/blob/v1.13.0/scipy/optimize/_slsqp_py.py, it looks the ftol parameter is passed as the acc parameter to the fortran SLSQP routine in here: https://github.com/scipy/scipy/blob/v1.13.0/scipy/optimize/slsqp/slsqp_optmz.f

I don't know fortran, but I guess that the termination criteria is defined in this line:

      IF ((ABS(f-f0).LT.acc .OR. dnrm2_(n,s,1).LT.acc) .AND. h3.LT.acc
     *     .AND. .NOT. badlin .AND. f .EQ. f)

This implies that acc is used in multiple ways:

The absolute difference between the current objective function value (f) and the previous value (f0) is less than acc, OR
The norm of some value s (could be the gradient direction of search) is less than acc.
Some value h3 is less than acc. No idea what this is.