Geodesic
Estimation of the error in convex polynomial optimization problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 2, pp. 200-216 
V. N. Nefedov. Estimation of the error in convex polynomial optimization problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 2, pp. 200-216. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_2_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Some error estimates are presented (in terms of the objective functional) for convex polynomial optimization problems. These estimates are based on certain necessary and sufficient conditions for polynomials to have a local minimum and on a study of the properties of locally convex polynomials.

[1] Fedorov V. V., Chislennye metody maksimina, Nauka, M., 1979 | MR

[2] Nefedov V. N., “O regulyarizatsii leksikograficheskikh zadach metodom minimalnykh “ustupok””, Zh. vychisl. matem. i matem. fiz., 23:6 (1983), 1326–1340 | MR | Zbl

[3] Nefedov V. Ya., “Polinomialnye zadachi optimizatsii”, Zh. vychisl. matem. i matem. fiz., 27:5 (1987), 661–675 | MR | Zbl

[4] Nefedov V. N., Metod isklyucheniya peremennykh v polinomialnykh zadachakh optimizatsii, Dep. v VINITI, No 7590–84, 1984

[5] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P. i dr., Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969 | MR

[6] Belousov E. G., Bank B. (red.), Matematicheskaya optimizatsiya: voprosy razreshimosti i ustoichivosti, Izd-vo MGU, M., 1986

[7] Nefedov V. I., Metody svedeniya zadachi vypuklogo programmirovaniya, ne udovletvoryayuschei usloviyu Sleitera, k zadache vypuklogo programmirovaniya, udovletvoryayuschei usloviyu Sleitera, Dep. v VINITI, No 2092-V88, 1988