Geodesic
Regular Self-Proximal Distances are Bregman
Journal of convex analysis, Tome 24 (2017) no. 1, pp. 135-148
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

Bregman distances play a key role in generalized versions of the proximal algorithm. This paper proposes a new characterization of Bregman distances in terms of their gradient and Hessian matrix. Thanks to this characterization, we obtain two results: all the so called self-proximal distances are Bregman, and all the induced proximal distances, under some regularity assumptions, are Bregman functions. 
@article{JCA_2017_24_1_JCA_2017_24_1_a10,
     author = {F. Alvarez and R. Correa and M. Marechal},
     title = {Regular {Self-Proximal} {Distances} are {Bregman}},
     journal = {Journal of convex analysis},
     pages = {135--148},
     year = {2017},
     volume = {24},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a10/}
}
TY  - JOUR
AU  - F. Alvarez
AU  - R. Correa
AU  - M. Marechal
TI  - Regular Self-Proximal Distances are Bregman
JO  - Journal of convex analysis
PY  - 2017
SP  - 135
EP  - 148
VL  - 24
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a10/
ID  - JCA_2017_24_1_JCA_2017_24_1_a10
ER  - 
%0 Journal Article
%A F. Alvarez
%A R. Correa
%A M. Marechal
%T Regular Self-Proximal Distances are Bregman
%J Journal of convex analysis
%D 2017
%P 135-148
%V 24
%N 1
%U http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a10/
%F JCA_2017_24_1_JCA_2017_24_1_a10
F. Alvarez; R. Correa; M. Marechal. Regular Self-Proximal Distances are Bregman. Journal of convex analysis, Tome 24 (2017) no. 1, pp. 135-148. http://geodesic.mathdoc.fr/item/JCA_2017_24_1_JCA_2017_24_1_a10/