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New Second-Order Bounds on the Expectation of Saddle Functions with Applications to Stochastic Linear Programming

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  • N. C. P. Edirisinghe

    (University of Tennessee, Knoxville, Tennessee)

Abstract

This paper develops new bounds on the expectation of a convex-concave saddle function of a random vector with compact domains. The bounds are determined by replacing the underlying distribution by unique discrete distributions, constructed using second-order moment information. The results extend directly to new second moment lower bounds in closed-form for the expectation of a convex function. These lower bounds are better than Jensen's bound, the only previously known lower bound for the convex case, under limited moment information. Application of the second moment bounds to two-stage stochastic linear programming is reported. Computational experiments, using randomly generated stochastic programs, indicate that the new bounds may easily outperform the usual first-order bounds.

Suggested Citation

  • N. C. P. Edirisinghe, 1996. "New Second-Order Bounds on the Expectation of Saddle Functions with Applications to Stochastic Linear Programming," Operations Research, INFORMS, vol. 44(6), pages 909-922, December.
    • Handle: RePEc:inm:oropre:v:44:y:1996:i:6:p:909-922
    DOI: 10.1287/opre.44.6.909
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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. Frauendorfer, Karl & Schurle, Michael, 2003. "Management of non-maturing deposits by multistage stochastic programming," European Journal of Operational Research, Elsevier, vol. 151(3), pages 602-616, December.
    3. David P. Morton & R. Kevin Wood, 1999. "Restricted-Recourse Bounds for Stochastic Linear Programming," Operations Research, INFORMS, vol. 47(6), pages 943-956, December.

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