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The Algorithm

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 tex2html_wrap_inline3373, 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].


next up previous contents
Next: A Numerical Study Up: Optimization Previous: Constraints

Joerg Fliege
Wed Dec 22 12:25:31 CET 1999