Geodesic
Dual interior point methods for linear semidefinite programming problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 12, pp. 2158-2180 
V. G. Zhadan; A. A. Orlov. Dual interior point methods for linear semidefinite programming problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 12, pp. 2158-2180. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_12_a3/
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     title = {Dual interior point methods for linear semidefinite programming problems},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Dual interior point methods for solving linear semidefinite programming problems are proposed. These methods are an extension of dual barrier-projection methods for linear programs. It is shown that the proposed methods converge locally at a linear rate provided that the solutions to the primal and dual problems are nondegenerate.

[1] Nesterov Yu. E., Nemirovski A. S., Interior point polynomial algorithms in convex programming, SIAM Publcations, Philadelphia, 1994 | MR | Zbl

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

[3] Todd M. J., “Semidefinite optimization”, Acta Numer., 10 (2001), 515–560 | DOI | MR | Zbl

[4] Laurent M., Rendle F., “Semidefinite programming and integer programming”, Discrete optimization. Hand bookd Operat. Res. and Management. Sci., Elsevier, Amsterdam, 2002

[5] H. Wolkowicz, R. Saigal, L. Vandenberghe, Handbook of semidefinite programming, Kluwer Acad. Publs, Boston, 2000 | MR

[6] De Klerk E., Aspects of semidefinite programming. Interior point algorithsm and selected applications, Kluwer Acad. Publs, Dordrecth, 2004 | MR

[7] Alizadeh F., “Interior point methods in semidefinite programming with applications to combinatiorial optimization”, SIAM J. Optimizat., 5 (1995), 13–51 | DOI | MR | Zbl

[8] Monteiro R. D. C., “Primal-dual path-following algorithms for semidefinite programming”, SIAM J. Optimizat., 7 (1997), 663–678 | DOI | MR | Zbl

[9] Monteiro R. D. C., “First- and second-order methods for semidefinite programming”, Math. Program. Ser. B, 97:1–2 (2003), 209–244 | MR | Zbl

[10] Dikin I. I., “Skhodimost posledovatelnosti vektorov dvoistvennykh peremennykh pri issledovanii odnoi zadachi poluopredelennogo programmirovaniya”, Kibernetika i sistemnyi analiz, 2003, no. 2, 156–163 | MR | Zbl

[11] Polyak B. T., Scherbakov P. S., “Randomizirovannyi metod resheniya zadachi poluopredelennogo programmirovaniya”, Stokhastich. optimizatsiya v informatike, 2:1 (2006), 38–70 | MR

[12] Evtushenko Yu. G., Zhadan V. G., “Dvoistvennye barerno-proektivnye i barerno-nyutonovskie metody dlya lineinogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 36:7 (1996), 30–45 | MR | Zbl

[13] Babynin M. S., Zhadan V. G., “Pryamoi metod vnutrennei tochki dlya lineinoi zadachi poluopredelennogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 48:10 (2008), 1780–1801 | MR | Zbl

[14] Muramatsu M., “Affine scaling algorithm fails for semidefinite programming”, Math. Program., 83 (1998), 393–406 | MR | Zbl

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

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

[17] Tyrtyshnikov E. E., Matrichnyi analiz i lineinaya algebra, Fizmatlit, M., 2007

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

[19] Alizadeh F., Haeberly J.-P. F., Overton M. L., “Complementarity and nondegeneracy in semidefinite programming”, Math. Program. Series B, 7:2 (1997), 129–162 | MR

[20] Ortega Dzh., Reinboldt V., Iteratsionnye metody resheniya sistem nelineinykh uravnenii so mnogimi neizvestnymi, Mir, M., 1975