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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
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.
Received: 06.10.2020
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
Linking options:
https://www.mathnet.ru/eng/bgumi72 https://www.mathnet.ru/eng/bgumi/v3/p17
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Abstract page: | 79 | Full-text PDF : | 37 | References: | 18 |
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