Generalized Chebyshev Bounds via Semidefinite Programming

Generalized Chebyshev Bounds via Semidefinite Programming

A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed using convex optimization. This result generalizes Chebyshev's inequality for scalar random variables. Two semidefinite programming for...

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Bibliographische Detailangaben
Veröffentlicht in:SIAM Review. - Society for Industrial and Applied Mathematics, 1959. - 49(2007), 1, Seite 52-64
1. Verfasser: Vandenberghe, Lieven (VerfasserIn)
Weitere Verfasser: Boyd, Stephen, Comanor, Katherine
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2007
Zugriff auf das übergeordnete Werk:SIAM Review
Schlagworte:semidefinite programming convex optimization duality theory Chebyshev inequalities moment problems Mathematics Philosophy
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520 |a A sharp lower bound on the probability of a set defined by quadratic inequalities, given the first two moments of the distribution, can be efficiently computed using convex optimization. This result generalizes Chebyshev's inequality for scalar random variables. Two semidefinite programming formulations are presented, with a constructive proof based on convex optimization duality and elementary linear algebra. 
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