A Smooth Monte Carlo Approach to Joint Chance Constrained Programs

We study joint chance constrained programs (JCCPs). JCCPs are often non-convex and non-smooth, and thus are generally challenging to solve. In this paper, we propose a logarithmsum-exponential smoothing technique to approximate a joint chance constraint by the difference of two smooth convex functions and use a sequential convex approximation algorithm, coupled with a Monte Carlo method, to solve the approximation. We call our approach a smooth Monte Carlo approach. We show that our approach is capable of handling both smooth and nonsmooth JCCPs where the random variables can be either continuous or discrete or mixed. The numerical experiments further confirm our findings.