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

Graduate Program in Operations Research, The University of Texas at Austin, Austin, Texas 78712
Graduate Program in Operations Research, The University of Texas at Austin, Austin, Texas 78712
steftcho{at}msn.com
morton{at}mail.utexas.edu

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.

Key Words: stochastic programming approximations; generalized moment problems
History: Received: February 26, 2001; revision received: June 7, 2003;revision received: August 9, 2004;