Filtering Domains of Factorable Functions using Interval Contractors

Laurent Granvilliers (1)

1 LS2N - Laboratoire des Sciences du Numérique de Nantes

Many theorems in mathematics require a real function to be continuous over the domain under consideration. In particular the Brouwer fixed point theorem and the mean value theorem underlie many interval methods like Newton operators for solving numerical constraint satisfaction problems or global optimization problems. Since the continuity property collapses when the function is not defined at some point it is then important to check whether the function is defined everywhere in a given domain. We introduce here an interval branch-and-contract algorithm that rigorously approximate the domain of definition of a fac-torable function within a box. The proposed approach mainly relies on interval contractors applied to the domain constraints and their negations stemming from the expression of the function.

Domaines: Logiciel mathématique [cs.MS]; Recherche opérationnelle [math.OC]; Analyse numérique [cs.NA]

Laurent Granvilliers. Filtering Domains of Factorable Functions using Interval Contractors. World Congress on Global Optimization, Jul 2019, Metz, France. ⟨hal-02476009⟩