Bounds for Probabilistic Programming with Application to a Blend Planning Problem

In this paper, we derive deterministic inner approximations for single and joint probabilistic constraints based on classical inequalities from probability theory such as the one-sided Chebyshev inequality, Bernstein inequality, Chernoff inequality and Hoeffding inequality (see Pinter 1989). New assumptions under which the bounds based approximations are convex allowing to solve the problem efficiently are derived. … Read more