Mots-clés : local convergence.
@article{TIMM_2013_19_2_a14,
author = {V. G. Zhadan and A. A. Orlov},
title = {Primal-dual {Newton} method for a~linear problem of semidefinite programming},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {157--169},
year = {2013},
volume = {19},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a14/}
}
TY - JOUR AU - V. G. Zhadan AU - A. A. Orlov TI - Primal-dual Newton method for a linear problem of semidefinite programming JO - Trudy Instituta matematiki i mehaniki PY - 2013 SP - 157 EP - 169 VL - 19 IS - 2 UR - http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a14/ LA - ru ID - TIMM_2013_19_2_a14 ER -
V. G. Zhadan; A. A. Orlov. Primal-dual Newton method for a linear problem of semidefinite programming. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 157-169. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a14/
[1] Eremin I. I., Teoriya lineinoi optimizatsii, Izd-vo “Ekaterinburg”, Ekaterinburg, 1999, 312 pp.
[2] Eremin I. I., Mazurov V. D., Astafev N. N., Nesobstvennye zadachi lineinogo i vypuklogo programmirovaniya, Nauka, M., 1983, 336 pp. | MR
[3] H. Wolkowicz, R. Saigal, L. Vandenberghe (eds.), Handbook of semidefinite programming, Kluwer Acad. Publ., Dordrecht, 2000, 656 pp. | MR
[4] de Klerk E., Aspects of semidefinite programming. Interior point algorithms and selected applications, Kluwer Acad. Publ., Dordrecht, 2004, 300 pp. | MR
[5] Alizadeh F., Haeberly J.-P. F., Overton M. L., “Primal-dual interior point methods for semidefinite programming. Convergence rates, stability and numerical results”, SIAM J. Optim., 8:3 (1998), 746–768 | DOI | MR | Zbl
[6] Nesterov Y. E., Todd M. J., “Primal-dual interior point methods for self-scaled cones”, SIAM J. Optim., 8:2 (1998), 324–364 | DOI | MR | Zbl
[7] Monteiro R. D. C., “Primal-dual path-following algorithms for semidefinite programming”, SIAM J. Optim., 7:3 (1997), 663–678 | DOI | MR | Zbl
[8] Muramatsu M., Vanderbei R. J., “Primal-dual affine scaling algorithms fails for semidefinite programming”, Math. Oper. Res., 24:1 (1999), 149–175 | DOI | MR | Zbl
[9] Evtushenko Yu. G., Zhadan V. G., Cherenkov A. P., “Primenenie metoda Nyutona k resheniyu zadach lineinogo programmirovaniya”, Zhurn. vychisl. matematiki i mat. fiziki, 35:6 (1995), 850–866 | MR | Zbl
[10] Magnus J. R., Neudecker H., “The elimination matrix: some lemmas and applications”, SIAM J. Alg. Disc. Methods, 1:4 (1980), 422–449 | DOI | MR | Zbl
[11] Arnold V. I., “O matritsakh, zavisyaschikh ot parametrov”, Uspekhi mat. nauk, 26:2(158) (1971), 101–114 | MR | Zbl
[12] Alizadeh F., Haeberly J.-P. F., Overton M. L., “Complementarity and nondegeneracy in semidefinite programming”, Math. Programming Ser. B, 77:2 (1997), 111–128 | MR | Zbl
[13] Ortega Dzh., Reinboldt V., Iteratsionnye metody resheniya sistem nelineinykh uravnenii so mnogimi neizvestnymi, Mir, M., 1975, 560 pp.
[14] Zhadan V. G., Orlov A. A., “O skhodimosti dvoistvennogo metoda Nyutona dlya lineinoi zadachi poluopredelennogo programmirovaniya”, Izv. Irkut. gos. un-ta. Matematika, 4:2 (2011), 75–90 | Zbl