Bounds for stochastic convex programs

Summary

A maximization of a concave function subject to convex inequalities is considered when the right-hand side of the inequalities is a random vector. Bounds are established for the distribution function of the optimum under these general assumptions for the normally and uniformly distributed right-hand 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.