Geodesic
Dykstra's Algorithm as the Nonlinear Extension of Bregman's Optimization Method
Journal of convex analysis, Tome 6 (1999) no. 2, pp. 319-334 Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

We show that Dykstra's algorithm with Bregman projections, which finds the Bregman projection of a point onto the nonempty intersection of finitely many closed convex sets, is actually the nonlinear extension of Bregman's primal-dual, dual coordinate ascent, row-action minimization algorithm. Based on this observation we give an alternative convergence analysis and a new geometric interpretation of Dykstra's algorithm with Bregman projections which complements recent work of Censor and Reich, Bauschke and Lewis, and Tseng.
Classification : 47N10, 49M30, 90C20
Mots-clés : Bregman projection, convex programming, Dykstra's algorithm 
@article{JCA_1999_6_2_JCA_1999_6_2_a4,
     author = {L. M. Bregman and Y. Censor and S. Reich},
     title = {Dykstra's {Algorithm} as the {Nonlinear} {Extension} of {Bregman's} {Optimization} {Method}},
     journal = {Journal of convex analysis},
     pages = {319--334},
     year = {1999},
     volume = {6},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_1999_6_2_JCA_1999_6_2_a4/}
}
TY  - JOUR
AU  - L. M. Bregman
AU  - Y. Censor
AU  - S. Reich
TI  - Dykstra's Algorithm as the Nonlinear Extension of Bregman's Optimization Method
JO  - Journal of convex analysis
PY  - 1999
SP  - 319
EP  - 334
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JCA_1999_6_2_JCA_1999_6_2_a4/
ID  - JCA_1999_6_2_JCA_1999_6_2_a4
ER  - 
%0 Journal Article
%A L. M. Bregman
%A Y. Censor
%A S. Reich
%T Dykstra's Algorithm as the Nonlinear Extension of Bregman's Optimization Method
%J Journal of convex analysis
%D 1999
%P 319-334
%V 6
%N 2
%U http://geodesic.mathdoc.fr/item/JCA_1999_6_2_JCA_1999_6_2_a4/
%F JCA_1999_6_2_JCA_1999_6_2_a4
L. M. Bregman; Y. Censor; S. Reich. Dykstra's Algorithm as the Nonlinear Extension of Bregman's Optimization Method. Journal of convex analysis, Tome 6 (1999) no. 2, pp. 319-334. http://geodesic.mathdoc.fr/item/JCA_1999_6_2_JCA_1999_6_2_a4/