JUCS - Journal of Universal Computer Science 4(6): 589-603, doi: 10.3217/jucs-004-06-0589
Enclosure Methods for Multivariate Differentiable Functions and Application to Global Optimization
expand article infoFrédéric Messine‡, Jean-Louis Lagouanelle§
‡ Lab. LIA, Departement d'Informatique de l'Université de Pau, France§ Lab. LIMA, Institut de Recherche en Informatique de Toulouse, Toulouse, France

Corresponding author: Frédéric Messine ( messine@univ-pau.fr )

© Frédéric Messine, Jean-Louis Lagouanelle.
This article is freely available under the J.UCS Open Content License.
Citation: Messine F, Lagouanelle J-L (1998) Enclosure Methods for Multivariate Differentiable Functions and Application to Global Optimization. JUCS - Journal of Universal Computer Science 4(6): 589-603. https://doi.org/10.3217/jucs-004-06-0589
Open Access
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
global optimization, interval arithmetic, multivariate functions, branch and bound algorithm, Taylor s expansion, polyhedral cone