Geodesic
Direct newton method for a linear problem of semidefinite programming
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 2, pp. 67-80 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a linear problem of semidefinite programming. To solve this problem, we propose a direct Newton method, which is a generalization of the direct barrier-Newton method for problems of linear programming. We study properties of the method and prove its local convergence. 
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V. G. Zhadan. Direct newton method for a linear problem of semidefinite programming. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 14 (2008) no. 2, pp. 67-80. http://geodesic.mathdoc.fr/item/TIMM_2008_14_2_a7/

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

[2] H. Wolkowicz, R. Saigal, L. Vandenberghe (eds.), Handbook of semidefinite programming, Kluwer Acad. Publ., Dordrecht, 2000 | MR

[3] Laurent M., Rendle F., “Semidefinite programming and integer programming”, Discrete optimization, Handbooks in Operations Research and Management Science, 12, eds. K. Aardal, G. Nemhauser, R. Weismantel, Elsevier, Amsterdam, 2005, 393–514 | Zbl

[4] Klerk E., de, Aspects of semidefinite programming. Interior point algorithms and selected applications, Kluwer Acad. Publ., Dordrecht, 2004 | MR

[5] Babynin M. S., Zhadan V. G., Barerno-proektivnyi metod dlya poluopredelennogo programmirovaniya. Soobscheniya po prikladnoi matematike, VTs RAN, M., 2007 | MR

[6] Evtushenko Yu., Zhadan V., “Stable barrier-projection and barrier-newton methods in linear programming”, Comput. Optimiz. and Appl., 3 (1994), 289–304 | DOI | MR

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

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

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

[10] 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

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