Abstract
Use of the semidefinite relaxation in the problem of sign-definiteness of the quadratic form under quadratic constraints enables one to establish from the duality conditions an S-procedure. However, the S-procedure giving the necessary and sufficient conditions for signdefiniteness of the relaxed problem provides only the sufficient conditions for sign-definiteness for the original problem for the case of two and more quadratic constraints. This property is called the deficiency of S-procedure. A method was proposed enabling one in some cases to establish the conditional sign-definiteness in the case where the S-procedure provides a negative result. This method give the necessary and sufficient conditions for sign-definiteness in the two-dimensional case. An example was given.
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Original Russian Text © L.B. Rapoport, 2018, published in Avtomatika i Telemekhanika, 2018, No. 11, pp. 150–158.
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Rapoport, L.B. Semidefinite Relaxation and New Conditions for Sign-Definiteness of the Quadratic Form under Quadratic Constraints. Autom Remote Control 79, 2073–2079 (2018). https://doi.org/10.1134/S0005117918110103
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DOI: https://doi.org/10.1134/S0005117918110103