The Demyanov metric and some other metrics in the family of convex sets
Open Mathematics (2012)
- Volume: 10, Issue: 6, page 2229-2239
- ISSN: 2391-5455
Access Full Article
top
Abstract
topHow to cite
topTadeusz Rzeżuchowski. "The Demyanov metric and some other metrics in the family of convex sets." Open Mathematics 10.6 (2012): 2229-2239. <http://eudml.org/doc/269366>.
@article{TadeuszRzeżuchowski2012,
abstract = {We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.},
author = {Tadeusz Rzeżuchowski},
journal = {Open Mathematics},
keywords = {Demyanov metric; Hausdorff metric; Convex sets; Small changes of sets; convex sets; small changes of sets},
language = {eng},
number = {6},
pages = {2229-2239},
title = {The Demyanov metric and some other metrics in the family of convex sets},
url = {http://eudml.org/doc/269366},
volume = {10},
year = {2012},
}
TY - JOUR
AU - Tadeusz Rzeżuchowski
TI - The Demyanov metric and some other metrics in the family of convex sets
JO - Open Mathematics
PY - 2012
VL - 10
IS - 6
SP - 2229
EP - 2239
AB - We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.
LA - eng
KW - Demyanov metric; Hausdorff metric; Convex sets; Small changes of sets; convex sets; small changes of sets
UR - http://eudml.org/doc/269366
ER -
References
top- [1] Aubin J.-P., Cellina A., Differential Inclusions, Grundlehren Math. Wiss., 264, Springer, Berlin, 1984 http://dx.doi.org/10.1007/978-3-642-69512-4[Crossref]
- [2] Baier R., Farkhi E.M., Differences of convex compact sets in the space of directed sets I. The space of directed sets, Set-Valued Anal., 2001, 9(3), 217–245 http://dx.doi.org/10.1023/A:1012046027626[Crossref] Zbl1097.49507
- [3] Demyanov V.F., Rubinov A.M., Constructive Nonsmooth Analysis, Approximation & Optimization, 7, Peter Lang, Frankfurt am Main, 1995 Zbl0887.49014
- [4] Demyanov V.F., Rubinov A.M. (Eds.), Quasidifferentiability and Related Topics, Nonconvex Optim. Appl., 43, Kluwer, Dordrecht, 2000
- [5] Diamond P., Kloeden P., Rubinov A., Vladimirov A., Comparative properties of three metrics in the space of compact convex sets, Set-Valued Anal., 1997, 5(3), 267–289 http://dx.doi.org/10.1023/A:1008667909101[Crossref] Zbl0895.90151
- [6] Grzybowski J., Lesniewski A., Rzezuchowski T., The completion of the space of convex, bounded sets with respect to the Demyanov metric, Demonstratio Math. (in press) Zbl1290.52004
- [7] Lesniewski A., Rzezuchowski T., The Demyanov metric for convex, bounded sets and existence of Lipschitzian Selectors, J. Convex Anal., 2011, 18(3), 737–747 Zbl1227.52002
- [8] Plis A., Uniqueness of optimal trajectories for non-linear control systems, Ann. Polon. Math., 1975, 29(4), 397–401 Zbl0316.49029
- [9] Schneider R., Convex Bodies: The Brunn-Minkowski Theory, Encyclopedia Math. Appl., 44, Cambridge University Press, Cambridge, 1993 http://dx.doi.org/10.1017/CBO9780511526282[Crossref] Zbl0798.52001
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.