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Second-Order Lower Bounds on the Expectation of a Convex Function

We develop a class of lower bounds on the expectation of a convex function. The bounds utilize the first two moments of the underlying random variable, whose support is contained in a bounded interval or hyperrectangle. Our bounds have applications to stochastic programs whose random parameters are known only through limited-moment information. Computational results are presented for two-stage stochastic linear programs.