A Tchebysheff-Type Bound on the Expectation of Sublinear Polyhedral Functions

José H. Dulá and Rajluxmi V. Murthy
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José H. Dulá: Southern Methodist University, Dallas, Texas
Rajluxmi V. Murthy: Southern Methodist University, Dallas, Texas

Operations Research, 1992, vol. 40, issue 5, 914-922

Abstract: 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.

Keywords: programming; infinite dimensional; stochastic: upper bounds on the recourse function; functional approximations (search for similar items in EconPapers)
Date: 1992
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