Geodesic
On deformations of nonsmooth optimization problems having an isolated extremal
Izvestiya. Mathematics, Tome 45 (1995) no. 1, pp. 187-195 
V. I. Skalyga. On deformations of nonsmooth optimization problems having an isolated extremal. Izvestiya. Mathematics, Tome 45 (1995) no. 1, pp. 187-195. http://geodesic.mathdoc.fr/item/IM2_1995_45_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A deformation method is presented for investigating optimization problems with Lipschitz functionals on a Banach space. A deformation minimum principle is proved: under a special nondegenerate deformation of an optimization problem the property of being a local minimum point is preserved for an extremal if the corresponding extremal of the standard problem had that property.

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

[2] N. A. Bobylev, “O deformatsionnom metode issledovaniya funktsionalov kachestva sistem s beskonechnym chislom stepenei svobody”, Avtomatika i Telemekhanika, 1981, no. 7, 11–13 | MR

[3] N. A. Bobylev, “O deformatsii funktsionalov, imeyuschikh edinstvennuyu kriticheskuyu tochku”, Matem. zametki, 34:3 (1983), 387–398 | MR | Zbl

[4] N. A. Bobylev, “Deformatsionnyi metod issledovaniya zadach nelineinogo programmirovaniya. I”, Avtomatika i Telemekhanika, 1989, no. 7, 82–90 | MR | Zbl

[5] N. A. Bobylev, “Deformatsionnyi metod issledovaniya zadach nelineinogo programmirovaniya. II”, Avtomatika i Telemekhanika, 1989, no. 8, 24–33 | MR | Zbl

[6] N. A. Bobylev, G. V. Kondakov, “Deformatsionnyi metod issledovaniya negladkikh optimizatsionnykh zadach”, Avtomatika i Telemekhanika, 1991, no. 5, 46–57 | MR | Zbl

[7] V. I. Skalyga, “O deformatsionnom metode issledovaniya na uslovnyi minimum funktsionalov kachestva sistem s beskonechnym chislom stepenei svobody”, Avtomatika i Telemekhanika, 1991, no. 6, 47–55 | MR | Zbl

[8] Zh. P. Oben, I. Ekland, Prikladnoi nelineinyi analiz, Mir, M., 1988 | MR

[9] N. Danford, Dzh. T. Shvarts, Lineinye operatory, obschaya teoriya, IL, M., 1962