Geodesic
A feasible dual affine scaling steepest descent method for the linear semidefinite programming problem
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1248-1266 
V. G. Zhadan. A feasible dual affine scaling steepest descent method for the linear semidefinite programming problem. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1248-1266. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a3/
@article{ZVMMF_2016_56_7_a3,
     author = {V. G. Zhadan},
     title = {A feasible dual affine scaling steepest descent method for the linear semidefinite programming problem},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1248--1266},
     year = {2016},
     volume = {56},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a3/}
}
TY  - JOUR
AU  - V. G. Zhadan
TI  - A feasible dual affine scaling steepest descent method for the linear semidefinite programming problem
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 1248
EP  - 1266
VL  - 56
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a3/
LA  - ru
ID  - ZVMMF_2016_56_7_a3
ER  - 
%0 Journal Article
%A V. G. Zhadan
%T A feasible dual affine scaling steepest descent method for the linear semidefinite programming problem
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 1248-1266
%V 56
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a3/
%G ru
%F ZVMMF_2016_56_7_a3

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

The linear semidefinite programming problem is considered. The dual affine scaling method in which all current iterations belong to the feasible set is proposed for its solution. Moreover, the boundaries of the feasible set may be reached. This method is a generalization of a version of the affine scaling method that was earlier developed for linear programs to the case of semidefinite programming.

[1] Wolkowicz Q., Saigal R., Vandenberghe L. (eds.), Handbook of semidefinite programming, Kluwer Academic Publishers, Boston–Dordrecht–London, 2000 | MR

[2] Zhadan V. G., Orlov A. A., “Dvoistvennye metody vnutrennei tochki dlya lineinoi zadachi poluopredelennogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 51:12 (2011), 2158–2180 | MR | Zbl

[3] Zhadan V. G., “Konechnye barerno-proektivnye metody dlya lineinogo programmirovaniya”, Metody optimizatsii i prilozheniya, 11-ya Baikalskaya mezhdunarodnaya shkola-seminar, Tr. konferentsii, plenarnye doklady (Irkutsk, 1998), 140–144

[4] Lasserre J. B., “Linear programming with positive semi-definite matreces”, MPE, 2 (1996), 499–522 | Zbl

[5] Kosolap A. I., “Simpleks-metod dlya resheniya zadach poluopredelennogo programmirovaniya”, Vestnik Donetskogo nats. un-ta. Ser. A: Estestvennye nauki, 2009, no. 2, 365–369

[6] Magnus J. R., Neudecker Q., “The elimination matrix: some lemmas and applications”, SIAM J. Alg. Disc. Meth., 1:4 (1980), 422–449 | DOI | MR | Zbl

[7] Magnus Ya. R., Neidekker Ch., Matrichnoe differentsialnoe ischislenie s prilozheniyami k statistike i ekonometrike, Fizmatlit, M., 2002

[8] Alizadeh F., Khaeberly J.-P. A., Overton M. L., “Complementarity and nondegeneracy in semidefinite programming”, Mathematical Programming. Series B, 7:2 (1997), 129–162 | MR

[9] Arnold V. I., “O matritsakh, zavisyaschikh ot parametrov”, Uspekhi matem. nauk, 26:2(158) (1971), 101–114 | MR

[10] Potaki G., “On the rank of extreme matrices in semidefinite programs and the multiplicity of optimal eigenvalues”, Mathematics of Operation Research, 23:2 (1998), 339–358 | DOI | MR

[11] Godunov S. K., Sovremennye aspekty lineinoi algebry, Nauchnaya kniga, Novosibirsk, 1997