Usually, global optimization codes with guaranteed convergence require a large number of function evaluations. On the other hand, there are efficient optimization methods which exploit gradient information, but only the approximation of a local minimum can be expected. If, however, the underlying application model is expensive, if there are additional constraints, especially equality constraints, and if the existence of different local solutions is expected, then heuristic rules for successive switches from one local minimum to another are often the only applicable approach. For this specific situation, we present some simple ideas for cutting off a local minimum and to restart a new local optimization run. However, some safeguards are needed to stabilize the algorithm, since very little is usually known about the distribution of local minima. The paper introduces an approach where the nonlinear programs generated can be solved by any available black box software. For our implementation, a sequential quadratic programming code (NLPQLP) is chosen for local optimization. The usage of the code is outlined and we present some numerical results based on a set of 58 test examples found in the literature.

To download the report, click here: NLPQLG.pdf