New second-order bounds on the expectation of saddle functions with applications to stochastic linear programming

New second-order bounds on the expectation of saddle functions with applications to stochastic linear programming

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Article ID: iaor20003764
Country: United States
Volume: 44
Issue: 6
Start Page Number: 909
End Page Number: 922
Publication Date: Nov 1996
Journal: Operations Research
Authors:
Keywords: programming: probabilistic
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.

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