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.

Voir la notice de l'article provenant de la source Heldermann Verlag

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 
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     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},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {1999},
     url = {http://geodesic.mathdoc.fr/item/JCA_1999_6_2_JCA_1999_6_2_a4/}
}
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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/