On covering methods for d.c. optimization

Covering methods constitute a broad class of algorithms for solving multiva riate Global Optimization problems. In this note we show that, when the obj ective f is d.c. and a d.c. decomposition for f is known, the computational burden usually suffered by multivariate covering methods is significantly reduced. With this we extend to the (non-differentiable) d.c. case the cove ring method of Breiman and Cutler, showing that it is a particular case of the standard outer approximation approach. Our computational experience sho ws that this generalization yields not only more flexibility but also faste r convergence than the covering method of Breiman-Cutler.