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

Author

Listed:
  • José H. Dulá

    (Southern Methodist University, Dallas, Texas)

  • Rajluxmi V. Murthy

    (Southern Methodist University, Dallas, Texas)

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.

Suggested Citation

  • José H. Dulá & Rajluxmi V. Murthy, 1992. "A Tchebysheff-Type Bound on the Expectation of Sublinear Polyhedral Functions," Operations Research, INFORMS, vol. 40(5), pages 914-922, October.
    • Handle: RePEc:inm:oropre:v:40:y:1992:i:5:p:914-922
    DOI: 10.1287/opre.40.5.914
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    Cited by:

    1. Steftcho P. Dokov & David P. Morton, 2005. "Second-Order Lower Bounds on the Expectation of a Convex Function," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 662-677, August.
    2. Ioana Popescu, 2007. "Robust Mean-Covariance Solutions for Stochastic Optimization," Operations Research, INFORMS, vol. 55(1), pages 98-112, February.

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