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Journal of the Belarusian State University. Mathematics and Informatics, 2020, Volume 3, Pages 17–27
DOI: https://doi.org/10.33581/2520-6508-2020-3-17-27
(Mi bgumi72)
 

Differential equations and Optimal control

Linear semidefinite programming problems: regularisation and strong dual formulations

O. I. Kostyukovaa, T. V. Chemisovab

a Institute of Mathematics, National Academy of Sciences of Belarus, 11 Surhanava Street, Minsk 220072, Belarus
b University of Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal
References:
Abstract: Regularisation consists in reducing a given optimisation problem to an equivalent form where certain regularity conditions, which guarantee the strong duality, are fulfilled. In this paper, for linear problems of semidefinite programming (SDP), we propose a regularisation procedure which is based on the concept of an immobile index set and its properties. This procedure is described in the form of a finite algorithm which converts any linear semidefinite problem to a form that satisfies the Slater condition. Using the properties of the immobile indices and the described regularisation procedure, we obtained new dual SDP problems in implicit and explicit forms. It is proven that for the constructed dual problems and the original problem the strong duality property holds true.
Keywords: linear semidefinite programming; strong duality; normalised immobile index set; regularisation; constraint qualifications.
Funding agency Grant number
The Center for Research & Development in Mathematics and Applications
Portuguese Foundation for the Development of Science and Technology UIDB/04106/2020
National Academy of Sciences of Belarus, Ministry of Education of the Republic of Belarus
This work was partially supported by the state research program «Convergence» (task 1.3.01, Republic of Belarus), by Portuguese funds through the Center for Research and Development in Mathematics and Applications (CIDMA), and the Foundation for Science and Technology (FCT, project UIDB/04106/2020).
Received: 06.10.2020
Document Type: Article
UDC: 519.853.2
Language: English
Citation: O. I. Kostyukova, T. V. Chemisova, “Linear semidefinite programming problems: regularisation and strong dual formulations”, Journal of the Belarusian State University. Mathematics and Informatics, 3 (2020), 17–27
Citation in format AMSBIB
\Bibitem{KosChe20}
\by O.~I.~Kostyukova, T.~V.~Chemisova
\paper Linear semidefinite programming problems: regularisation and strong dual formulations
\jour Journal of the Belarusian State University. Mathematics and Informatics
\yr 2020
\vol 3
\pages 17--27
\mathnet{http://mi.mathnet.ru/bgumi72}
\crossref{https://doi.org/10.33581/2520-6508-2020-3-17-27}
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