Geodesic
Subdifferentiability and superdifferentiability of distance functions
Matematičeskie zametki, Tome 61 (1997) no. 4, pp. 530-542 
S. I. Dudov. Subdifferentiability and superdifferentiability of distance functions. Matematičeskie zametki, Tome 61 (1997) no. 4, pp. 530-542. http://geodesic.mathdoc.fr/item/MZM_1997_61_4_a4/
@article{MZM_1997_61_4_a4,
     author = {S. I. Dudov},
     title = {Subdifferentiability and superdifferentiability of distance functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {530--542},
     year = {1997},
     volume = {61},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_4_a4/}
}
TY  - JOUR
AU  - S. I. Dudov
TI  - Subdifferentiability and superdifferentiability of distance functions
JO  - Matematičeskie zametki
PY  - 1997
SP  - 530
EP  - 542
VL  - 61
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_4_a4/
LA  - ru
ID  - MZM_1997_61_4_a4
ER  - 
%0 Journal Article
%A S. I. Dudov
%T Subdifferentiability and superdifferentiability of distance functions
%J Matematičeskie zametki
%D 1997
%P 530-542
%V 61
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_4_a4/
%G ru
%F MZM_1997_61_4_a4

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

We obtain necessary and sufficient conditions for the subdifferentiability and superdifferentiability (in the Dem'yanov–Rubinov sense) of the distance in an arbitrary norm from a point to a set for the finitedimensional case. The geometric structure of the subdifferential and the superdifferential is described.

[1] Pshenichnyi B. N., Vypuklyi analiz i ekstremalnye zadachi, Nauka, M., 1980

[2] Demyanov V. F., Vasilev L. V., Nedifferentsiruemaya optimizatsiya, Nauka, M., 1981

[3] Demyanov V. F., Rubinov L. V., Osnovy negladkogo analiza i kvazidifferentsialnoe ischislenie, Nauka, M., 1990

[4] Klark F., Optimizatsiya i negladkii analiz, Nauka, M., 1988 | Zbl

[5] Minchenko L. I., Borisenko O. F., Gritsai S. P., Mnogoznachnyi analiz i vozmuschennye zadachi nelineinogo programmirovaniya, Navuka i tekhnika, Minsk, 1993 | Zbl

[6] Minchenko L. I., “Vychislenie subdifferentsialov marginalnykh funktsii s pomoschyu funktsii rasstoyaniya”, Kibernetika, 1989, no. 5, 83–85 | MR | Zbl

[7] Balaganskii V. S., “Dostatochnye usloviya differentsiruemosti metricheskoi funktsii”, Tr. IMM UrO RAN, 1, 84–89 | Zbl

[8] Dudov S. I., “Differentsiruemost po napravleniyam funktsii rasstoyaniya”, Matem. sb., 186:3 (1995), 29–52 | MR | Zbl

[9] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974 | Zbl