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A Tchebysheff-Type Bound on the Expectation of Sublinear Polyhedral Functions
José H. Dulá and Rajluxmi V. Murthy
Vol. 40, No. 5 (Sep. - Oct., 1992), pp. 914-922
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/171817
Page Count: 9
You can always find the topics here!Topics: Mathematical functions, Mathematical moments, Random variables, Mathematical problems, Objective functions, Approximation, Optimal solutions, Mathematics, Linear programming, Mathematical inequalities
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This work presents an upper bound on the expectation of sublinear polyhedral functions of multivariate random variables based on an inner linearization and domination by a quadratic function. The problem is formulated as a semi-infinite program which requires information on the first and second moments of the distribution, but without the need of an independence assumption. Existence of a solution and stability of this semi-infinite program are discussed. We show that an equivalent optimization problem with a nonlinear objective function and a set of linear constraints may be used to generate solutions.
Operations Research © 1992 INFORMS