Enclosure Methods for Multivariate Differentiable Functions and Application to Global Optimization

Frédéric Messine (Lab. LIA, Departement d'Informatique de l'Université de Pau, France)

Jean-Louis Lagouanelle (Lab. LIMA, Institut de Recherche en Informatique de Toulouse, France)

Abstract: The efficiency 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 defined on a box (right parallelepiped). The studied method provides a lower bound (or upper bound) of a function in that box throughout two different 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.

Keywords: Taylor s expansion, branch and bound algorithm, global optimization, interval arithmetic, multivariate functions, polyhedral cone