Generalized Chebyshev bounds via semidefinite programming
| Venue: | SIAM Review |
| Citations: | 7 - 1 self |
BibTeX
@ARTICLE{Vandenberghe_generalizedchebyshev,
author = {Lieven Vandenberghe and Stephen Boyd and Katherine Comanor},
title = {Generalized Chebyshev bounds via semidefinite programming},
journal = {SIAM Review},
year = {},
volume = {49}
}
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Abstract
Abstract. 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. Key words. Semidefinite programming, convex optimization, duality theory, Chebyshev inequalities, moment problems. AMS subject classifications. 90C22, 90C25, 60-08.
