Article

Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text
Advertising


Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 33,00 € Taxes included to order
    Pages Iconography Videos Other
    6 0 0 0


Comptes Rendus Mathématique
Volume 337, n° 1
pages 31-36 (juillet 2003)
Doi : 10.1016/S1631-073X(03)00267-X
accepted : 13 May 2003
Version continue de l'algorithme d'Uzawa
Continuous version of the Uzawa algorithm

Bertrand  Maury
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, boîte courrier 187, 75252 Paris cedex 05, France 

@@#100979@@

Nous avons proposé dans Carlier et al. (ESAIM Proceedings, CEMRACS 1999) un algorithme permettant d'approximer la projection d'une fonction   (où   est un domaine convexe) sur le cône des fonctions convexes. Cet algorithme est basé sur une expression duale de la contrainte de convexité, qui conduit à un problème de point-selle qui n'a pas de solution en général. Nous montrons ici que l'algorithme d'Uzawa appliqué à cette situation peut être vu comme une discrétisation semi-implicite d'une équation d'évolution du type   où   est une fonction convexe, propre, et s.c.i. Dans le cas où le problème de point-selle n'admet pas de solution, on a   Nous établissons que   diverge alors, mais qu'une sous-suite de la composante primale de la trajectoire converge faiblement vers la solution du problème de projection initial. Pour citer cet article : B. Maury, C. R. Acad. Sci. Paris, Ser. I 337 (2003).

Abstract

In Carlier et al. (ESAIM Proceedings, CEMRACS 1999), an algorithm was proposed to approximate the projection of a function   (where   is a convex domain) onto the cone of convex functions. This algorithm is based on a dual expression of the constraint, which leads to a saddle-point problem which has no solution in general. We show here that the Uzawa algorithm for this saddle-point problem can be seen as the semi-discretization of an evolution equation   where   is a convex, l.s.c., proper function. In case the saddle-point problem has no solution, one has   but  . We establish that   is then divergent, and that a subsequence of the associated trajectory in the primal space converges weakly to the solution of the initial projection problem. To cite this article: B. Maury, C. R. Acad. Sci. Paris, Ser. I 337 (2003).




© 2003  Académie des sciences@@#104156@@

EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Close
Article Outline
You can move this window by clicking on the headline