Generalized Chebyshev bounds via semidefinite programming

Lieven Vandenberghe

doi:10.1137/S0036144504440543

2007-01-01

Lieven Vandenberghe *

Stephen Boyd

Katherine Comanor

DOI：10.1137/S0036144504440543

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摘要

En 中文

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.

Keyword:

semidefinite programming

convex optimization

duality theory

Chebyshev inequalities

moment problems

期刊

SIAM Review

IF:

6.1

论文数:

888

被引数:

1.2W

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暂无机构信息

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