Semidefinite Relaxation and New Conditions for Sign-Definiteness of the Quadratic Form under Quadratic Constraints
- Авторы: Rapoport L.B.1
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Учреждения:
- Trapeznikov Institute of Control Sciences
- Выпуск: Том 79, № 11 (2018)
- Страницы: 2073-2079
- Раздел: Optimization, System Analysis, and Operations Research
- URL: https://journals.rcsi.science/0005-1179/article/view/151079
- DOI: https://doi.org/10.1134/S0005117918110103
- ID: 151079
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Аннотация
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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Об авторах
L. Rapoport
Trapeznikov Institute of Control Sciences
Автор, ответственный за переписку.
Email: LBRapoport@gmail.com
Россия, Moscow
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