A variant of the dual simplex method for a linear semidefinite programming problem
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 90-100 Cet article a éte moissonné depuis la source Math-Net.Ru

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A linear semidefinite programming problem in the standard statement is considered, and a variant of the dual simplex method is proposed for its solution. This variant generalizes the corresponding method for linear programming problems. The transfer from an extreme point of the feasible set to another extreme point is described. The convergence of the method is proved.
Keywords: linear semidefinite programming problem, dual problem, extreme points, dual simplex method.
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V. G. Zhadan. A variant of the dual simplex method for a linear semidefinite programming problem. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 90-100. http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a8/

[1] Eremin I.I., Teoriya lineinoi optimizatsii, Izd-vo “Ekaterinburg”, Ekaterinburg, 1999, 312 pp.

[2] Vasilev F.P., Ivanitskii A.Yu., Lineinoe programmirovanie, Faktorial Press, M., 2008, 347 pp. | MR

[3] Vandenberghe L., Boyd S., “Semidefinite programming”, SIAM Review, 38:1 (1996), 49–95 | DOI | MR | Zbl

[4] Handbook of Semidefinite Programming, eds. H. Wolkowicz, R. Saigal, L. Vandenberghe, Kluwer Acad. Publ., Dordrecht, 2000, 656 pp. | MR

[5] Lasserre J.B., “Linear programming with positive semi-definite matreces”, Math. Problems in Engineering, 2 (1996), 499–522 | DOI | Zbl

[6] Pataki G., “Cone-LP's and semidefinite programs: geometry and simplex-type method”, Proc. Conf. on Integer Programming and Combinatorial Optimization (IPCO 5), Vancouver, 1996, 1–13

[7] Kosolap A.I., “Simpleks-metod dlya resheniya zadach poluopredelennogo programmirovaniya”, Vestn. Donets. nats. un-ta. (Ser. A: Estestvennye nauki), 2009, no. 2, 365–369

[8] Zhadan V.G., “Ob odnom variante simpleks-metoda dlya lineinoi zadachi poluopredelennogo programmirovaniya”, Tr. In-ta matematiki i mekhaniki UrO RAN, 21:3 (2015), 117–127 | MR

[9] Magnus Ya.R., Neidekker Ch., Matrichnoe differentsialnoe ischislenie s prilozheniyami k statistike i ekonometrike, Fizmatlit, M., 2002, 496 pp.