TY: JOUR
T1 - Linear semidefinite programming problems: regularisation and strong dual formulations
A1 - Kostyukova, O. I.
A1 - Tchemisova, T. V.
N2 - 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.
UR - https://ria.ua.pt/handle/10773/30248
Y1 - 2020
PB - Belarusian State University