Enclosure Methods for Multivariate Differentiable Functions and Application to Global Optimization

The e ciency of global optimization methods in connection with interval arithmetic is no more to be demonstrated. They allow to determine the global optimum and the corresponding optimizers, with certainty and arbitrary accuracy. One of the main features of these algorithms is to deliver a function enclosure de ned on a box (right parallelepiped). The studied method provides a lower bound (or upper bound) of a function in that box throughout two di erent strategies. As we shall see, these algorithms associated with various Branch and Bound methods lead to accelerated convergence and permit to avoid the cluster problem.