At the present moment, an SQP-method [34] is used to solve
the location problem. Since in this SQP-method the Hessian of the Lagrangian
of the optimization problem is updated by way of a modified Pantoja-Mayne
update formula, only first-order information on the objective function and the
constraint functions is needed. This means that, in principle, the use of
approximations of order 3 to 
, as outlined in
Section 5.1.3, is unnecessarily accurate. However, other optimization
routines might benefit from this accuracy, and the bottleneck of the
computation does not lie in the gradient approximation anyway.
Of course, it is trivial to replace the optimization routine in use
with a different one.
Note that this optimization method is able to find local optimizers of the objective function, but cannot decide if a global optimizer is found. Any user of the software package is urged to rerun the code from several different starting points in order to make sure that the probability of finding the global optimum is increased. This multistart technique mimics, albeit roughly, the application of a clustering technique, one of the most well known and most successful global optimization approaches [23].