Abstract
In this article, we show that the algebraic degree in semidefinite programming can be expressed in terms of the coefficient of a certain monomial in a doubly symmetric polynomial. This characterization of the algebraic degree allows us to use the theory of symmetric polynomials to obtain many interesting results of Nie, Ranestad and Sturmfels in a simpler way.
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Acknowledgements
This research is supported by the 2021 Annual Research Program of the Da Lat University. The first author is partially funded by the Simons Foundation Grant Targeted for Institute of Mathematics, Vietnam Academy of Science and Technology. He would like to thank the institute for the very kind support and hospitality.
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Hiep, D.T., Giao, N.T.N. & Van, N.T.M. A characterization of the algebraic degree in semidefinite programming. Collect. Math. 74, 443–455 (2023). https://doi.org/10.1007/s13348-022-00358-5
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DOI: https://doi.org/10.1007/s13348-022-00358-5