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

Operations Research · 1992 · Volume 40 · Issue 5

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

Enable JavaScript for citation tools and additional paper interactions.