Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 61, 2012 - Issue 3
137
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Alternating proximal algorithms with asymptotically vanishing coupling. Application to domain decomposition for PDE's

&
Pages 307-325 | Received 13 Sep 2009, Accepted 03 Jul 2010, Published online: 05 Oct 2010

References

  • Acker , F and Prestel , MA . 1980 . Convergence d'un schéma de minimisation alternée . Ann. Faculté Sci. Toulouse V, Sér. Math. , 2 : 1 – 9 .
  • Adams , R . 1975 . Sobolev Spaces , New York : Academic Press .
  • Alvarez , F and Cominetti , R . 2002 . Primal and dual convergence of a proximal point exponential penalty method for linear programming . Math. Program. , 93 : 87 – 96 .
  • Attouch , H , Bolte , J , Redont , P and Soubeyran , A . 2008 . Alternating proximal algorithms for weakly coupled convex minimization problems. Applications to dynamical games and PDE's . J. Convex Anal. , 15 : 485 – 506 .
  • H. Attouch, A. Cabot, P. Frankel, and J. Peypouquet, Alternating proximal algorithms for constrained variational inequalities. Application to domain decomposition for PDE's, submitted to Nonlinear Analysis: Theory, Methods & Applications.
  • Attouch , H and Czarnecki , M-O . 2010 . Asymptotic behavior of coupled dynamical systems with multiscale aspects . J. Differential Eqns. , 248 : 1315 – 1344 .
  • Attouch , H , Redont , P and Soubeyran , A . 2007 . A new class of alternating proximal minimization algorithms with costs-to-move . SIAM J. Optim. , 18 : 1061 – 1081 .
  • Azé , D . 1997 . Eléments d'Analyse Convexe et Variationnelle , Paris : Ellipses .
  • Baillon , J-B and Cominetti , R . 2001 . A convergence result for non-autonomous subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming . J. Funct. Anal. , 187 : 263 – 273 .
  • Bauschke , HH , Combettes , P-L and Reich , S . 2005 . The asymptotic behavior of the composition of two resolvents . Nonlinear Anal. , 60 : 283 – 301 .
  • Brezis , H . 1999 . Analyse fonctionnelle: Théorie et Applications , Paris : Dunod .
  • Cabot , A . 2005 . Proximal point algorithm controlled by a slowly vanishing term: Applications to hierarchical minimization . SIAM J. Optim. , 15 : 555 – 572 .
  • Frankel , P . Alternating proximal algorithm with costs-to-move, dual description and application to PDE's . Discr. Cont. Dyn. Syst. Ser. S ,
  • Lions , J-L and Magenes , E . 1972 . “ Non-homogeneous boundary value problems and applications ” . In Die Grundlehren der mathematischen Wissenschaften , New York-Heidelberg : Springer-Verlag .
  • Marschall , J . 1987 . The trace of Sobolev-Slobodeckij spaces on Lipschitz domains . Manuscripta Math. , 58 : 47 – 65 .
  • Opial , Z . 1967 . Weak convergence of the sequence of successive approximations for nonexpansive mappings . Bull. Amer. Math. Soc. , 73 : 591 – 597 .
  • Raviart , P-A and Thomas , J-M . 1993 . Introduction à l'Analyse Numérique des Équations aux Dérivées Partielles , Paris : Masson .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.