Bounds for Stochastic Convex Programs
A maximization of a concave function subject to convex inequalities is considered when the righthand side of the inequalities are random variables. Bounds are established for the distribution function of the optimum under these general assumptions for the normally and uniformly distributed righthand sides. Four kinds of bounds are shown to be the best in the sense that in extreme cases they are equal to the actual probability function itself. The approach is demonstrated on a simple example and the influence of the problem-dimensionality is discussed. (Author).
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