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- W2186349712 abstract "Edmundson and Madansky have developed an upper bound for the expectation of a convex function of a multivariate random variable. The bound exists under rather general conditions. However, it is computable for n≥3 only when the random variables are independent. This paper develops a procedure for computing this bound using a linear program. We also show how to extend and sharpen the bound by utilizing it on subsets of the sample space. Moreover, the bound is applicable to arbitrary convex domains which may be unbounded. The new bounds along with Jensen’s Inequality may be applied on subsets using the procedures developed by Huang, Ziemba, and Ben-Tal to yield a procedure for obtaining upper and lower bounds on the expectation of a convex function of a multivariate random variable to an arbitrary degree of accuracy. The results are useful in a wide variety of optimization applications. Some numerical work is provided to illustrate the use of the new bounds." @default.
- W2186349712 created "2016-06-24" @default.
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- W2186349712 date "1986-01-01" @default.
- W2186349712 modified "2023-10-14" @default.
- W2186349712 title "A tight upper bound for the expectation of a convex function of a multivariate random variable" @default.
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- W2186349712 doi "https://doi.org/10.1007/bfb0121113" @default.
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