Geodesic
Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 397-417

Voir la notice de l'article provenant de la source Math-Net.Ru

A duality theory is developed to describe iterative methods for polyhedral approximation of convex bodies. The various types of approximation problems requiring the application of the duality theory are considered. Based on the theory, approximation methods can be designed for bodies with a dual description (in terms of the support/distance function) and methods can be developed that are optimal in terms of dual complexity characteristics of approximating polytopes (vertices/facets). New optimal methods based on the theory are formulated. 
@article{ZVMMF_2008_48_3_a4,
     author = {G. K. Kamenev},
     title = {Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {397--417},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a4/}
}
TY  - JOUR
AU  - G. K. Kamenev
TI  - Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 397
EP  - 417
VL  - 48
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a4/
LA  - ru
ID  - ZVMMF_2008_48_3_a4
ER  - 
%0 Journal Article
%A G. K. Kamenev
%T Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 397-417
%V 48
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a4/
%G ru
%F ZVMMF_2008_48_3_a4
G. K. Kamenev. Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 3, pp. 397-417. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_3_a4/