Initial Point for NLP models

This example was introduced to illustrate the need for good initial points in NLP models (see http://amsterdamoptimization.com/pdf/snopt.pdf).

The problem is just a three variable model: find the smallest enclosing circle around n points. GAMS has a default initial point of zero which is often very bad. Only IPOPT can find an optimal solution quickly. But if we add a good starting point, all solvers find the optimal very quickly. Even the performance of IPOPT improves.

For a presentation I cleaned up the example a little bit:

 

Note: actually the model is easier to solve using a slightly different formulation:

(i.e. minimize the square of the radius r).