Some convergence results for asynchronous algorithms

TLDR: In this article, the authors present convergence results for the asynchronous algorithms based essentially on the notion of classical contraction and generalize all convergence results of those algorithms which are based on the vectorial norm hypothesis.

Abstract: Nous presentons dans cet article des resultats de convergence des algorithmes asynchrones bases essentiellement sur la notion classique de contraction. Nous generalisons, en particulier, tous les resultats de convergence de ces algorithmes qui font l'hypothese de contraction en norme vectorielle qui recemment a ete tres souvant utilisee. Par ailleurs, l'hypothese de contraction en norme vectorielle peut se trouver difficile, voire impossible a verifier pour certains problemes qui peuvent etre cependant abordes dans le cadre de la contraction classique que nous adoptons. In this paper we present convergence results for the asynchronous algorithms based essentially on the notion of classical contraction. We generalize, in particular, all convergence results for those algorithms which are based on the vectorial norm hypothesis, in wide spread use recently. Certain problems, for which the vectorial norm hypothesis can be difficult or even impossible to verify, can nontheless be tackled within the scope of the classical contraction that we adopte.