Geodesic
Characteristic properties of primal exhausters for various classes of positively homogeneous functions
Trudy Instituta matematiki, Tome 19 (2011) no. 2, pp. 12-25.

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

The paper deals with the exhaustive families of upper convex approximations (the primal upper exhausters) and the exhaustive families of lower concave approximations (the primal lower exhausters) of positively homogeneous functions defined on finite dimensional vector spaces. We give a comprehensive description of characteristic properties of the primal upper and lower exhausters for Lipshitzian positively homogeneous functions as well as for difference-sublinear and piecewise linear functions. 
@article{TIMB_2011_19_2_a2,
     author = {V. V. Gorokhovik and M. A. Starovoitova},
     title = {Characteristic properties of primal exhausters for various classes of positively homogeneous functions},
     journal = {Trudy Instituta matematiki},
     pages = {12--25},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2011_19_2_a2/}
}
TY  - JOUR
AU  - V. V. Gorokhovik
AU  - M. A. Starovoitova
TI  - Characteristic properties of primal exhausters for various classes of positively homogeneous functions
JO  - Trudy Instituta matematiki
PY  - 2011
SP  - 12
EP  - 25
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TIMB_2011_19_2_a2/
LA  - ru
ID  - TIMB_2011_19_2_a2
ER  - 
%0 Journal Article
%A V. V. Gorokhovik
%A M. A. Starovoitova
%T Characteristic properties of primal exhausters for various classes of positively homogeneous functions
%J Trudy Instituta matematiki
%D 2011
%P 12-25
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TIMB_2011_19_2_a2/
%G ru
%F TIMB_2011_19_2_a2
V. V. Gorokhovik; M. A. Starovoitova. Characteristic properties of primal exhausters for various classes of positively homogeneous functions. Trudy Instituta matematiki, Tome 19 (2011) no. 2, pp. 12-25. http://geodesic.mathdoc.fr/item/TIMB_2011_19_2_a2/

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

[2] Demyanov V.F., Rubinov A.M., Osnovy negladkogo analiza i kvazidifferentsialnoe ischislenie, Nauka, M., 1990 | MR

[3] Demyanov V.F., “Exhausters of a positively hoomogeneous function”, Optimization, 45:1 (1999), 13–29 | DOI | MR | Zbl

[4] Demyanov V.F., “Exhausters and convexificators — new tools in nonsmooth analysis”, Quasidifferentiability and Related Topics, eds. Demyanov V.F. and Rubinov A.M., Kluwer Academic Publishers, Dordrecht, 2000, 85–137 | MR | Zbl

[5] Kutateladze S.S., Rubinov A.M., Dvoistvennost Minkovskogo i ee prilozheniya, Nauka, Novosibirsk, 1976 | MR

[6] Uderzo A., “Convex approximators, convexificators and exhausters: applications to constrained extremum problems”, Quasidifferentiability and Related Topics, eds. Demyanov V.F. and Rubinov A.M., Kluwer Academic Publishers, Dordrecht, 2000, 297–327 | MR | Zbl

[7] Demyanov V.F., Roshchina V.A., “Exhausters, optimality conditions and related problems”, J. of Global Optimization, 40:1–3 (2008), 71–85 | DOI | MR | Zbl

[8] Demyanov V.F., Roschina V.A., “Obobschennye subdifferentsialy i ekzostery v negladkom analize”, Doklady RAN, 416:1, 18–21

[9] Castellani M., “Dual representations of positively homogeneous functions”, Quasidifferentiability and Related Topics, eds. Demyanov V.F. and Rubinov A.M., Kluwer Academic Publishers, Dordrecht, 2000, 73–84 | MR | Zbl

[10] Castellani M., “Dual representation for proper positively homogeneous functions”, J. of Global Optimization, 16:4 (2000), 393–400 | DOI | MR | Zbl

[11] Demyanov V.F., Roshchina V.A., “Constrained optimality conditions in terms of upper and lower exhausters”, Appl. Comput. Math., 4:1 (2005), 25–35 | MR

[12] Demyanov V.F., Roshchina V.A., “Optimality conditions in terms of upper and lower exhausters”, Optimization, 55:5–6 (2006), 525–540 | DOI | MR | Zbl

[13] Demyanov V.F., Roshchina V.A., “Exhausters and subdifferentials in non-smooth analysis”, Optimization, 57:1 (2008), 41–56 | DOI | MR | Zbl

[14] Roshchina V., “Reducing exhausters”, J. Optim. Theory Appl., 136:2 (2008), 261–273 | DOI | MR | Zbl

[15] Abbasov M.E., Demyanov V.F., “Usloviya ekstremuma negladkoi funktsii v terminakh ekzosterov i koekzosterov”, Tr. In-ta matematiki i mekhaniki UrO RAN, 15:4 (2009), 10–19

[16] Aleksandrov P.S., Vvedenie v teoriyu mnozhestv i obschuyu topologiyu, Nauka, M., 1977 | MR

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

[18] Gorokhovik V.V., Gorokhovik S.Ya., “Kriterii globalnoi epilipshitsevosti mnozhestv”, Vestsi NAN Belarusi. Ser. fiz.-mat. navuk, 1995, no. 1, 118–120 | MR | Zbl

[19] Gorokhovik V.V., “O zvezdnosti mnozhestv na beskonechnosti”, Vestsi NAN Belarusi. Ser. fiz.-mat. navuk, 2001, no. 2, 5–8 | MR

[20] Lyusternik L.A., Sobolev V.I., Elementy funktsionalnogo analiza, Nauka, M., 1965 | MR

[21] Gorokhovik V.V., Vypuklye i negladkie zadachi vektornoi optimizatsii, Nauka i tekhnika, Minsk, 1990 | MR | Zbl

[22] Gorokhovik V.V., Zorko O.I., “Poliedralnaya kvazidifferentsiruemost veschestvennoznachnykh funktsii”, Doklady AN Belarusi, 36:5 (1992), 393–397 | MR | Zbl

[23] Gorokhovik V.V., Zorko O.I., “Piecewise affine functions and polyhedrel sets”, Optimization, 31:3 (1994), 209–221 | DOI | MR | Zbl

[24] Gorokhovik V.V., Zorko O.I., “Nevypuklye poliedralnye mnozhestva i funktsii i ikh analiticheskie predstavleniya”, Doklady AN Belarusi, 39:1 (1995), 5–9 | MR

[25] Rokafellar R., Vypuklyi analiz, Mir, M., 1973