Generalized Chebyshev bounds via semidefinite programming

被引：67
|
作者：
Vandenberghe, Lieven [1 ]
Boyd, Stephen
Comanor, Katherine
机构：
[1] Univ Calif Los Angeles, Dept Elect Engn, Los Angeles, CA 90024 USA
[2] Stanford Univ, Dept Elect Engn, Stanford, CA 94305 USA
[3] RAND Corp, Santa Monica, CA USA
来源：
SIAM REVIEW | 2007年 / 49卷 / 01期
关键词：
semidefinite programming; convex optimization; duality theory; Chebyshev inequalities; moment problems;
D O I：
10.1137/S0036144504440543
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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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页码：52 / 64
页数：13
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