Geodesic
Algorithms of minimization of Hausdorff deviation of a convex compact from a set of movable convex polygons
Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 2, pp. 218-232

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

We study the problem of finding the optimal location of a set of moving figures within the boundaries of a given convex set (arena) on the plane. The optimality criterion was chosen to minimize the Hausdorff deviation of the arena from the union of these moving objects. Numerical algorithms are proposed for solving the problem, based on dividing the arena into areas of influence of the figures (into generalized Dirichlet zones) and finding the optimal position of each of them within the boundaries of its area. When creating the algorithms, non-smooth optimization methods and the constructions of the geometric theory of approximations were used. A numerical simulation of the solution of the problem is performed for the case of three moving convex polygons.
Keywords: Hausdorff deviation, convex set, Chebyshev center, minimization, subdifferential. 
@article{CHFMJ_2020_5_2_a2,
     author = {P. D. Lebedev and A. A. Uspenskii and V. N. Ushakov},
     title = {Algorithms of minimization of {Hausdorff} deviation of a convex compact from a set of movable convex polygons},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {218--232},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a2/}
}
TY  - JOUR
AU  - P. D. Lebedev
AU  - A. A. Uspenskii
AU  - V. N. Ushakov
TI  - Algorithms of minimization of Hausdorff deviation of a convex compact from a set of movable convex polygons
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2020
SP  - 218
EP  - 232
VL  - 5
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a2/
LA  - ru
ID  - CHFMJ_2020_5_2_a2
ER  - 
%0 Journal Article
%A P. D. Lebedev
%A A. A. Uspenskii
%A V. N. Ushakov
%T Algorithms of minimization of Hausdorff deviation of a convex compact from a set of movable convex polygons
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2020
%P 218-232
%V 5
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a2/
%G ru
%F CHFMJ_2020_5_2_a2
P. D. Lebedev; A. A. Uspenskii; V. N. Ushakov. Algorithms of minimization of Hausdorff deviation of a convex compact from a set of movable convex polygons. Čelâbinskij fiziko-matematičeskij žurnal, Tome 5 (2020) no. 2, pp. 218-232. http://geodesic.mathdoc.fr/item/CHFMJ_2020_5_2_a2/