A smooth Monte Carlo approach to joint chance-constrained programs

This article studies Joint Chance-Constrained Programs (JCCPs). JCCPs are often non-convex and non-smooth and thus are generally challenging to solve. This article proposes a logarithm-sum-exponential smoothing technique to approximate a joint chance constraint by the difference of two smooth convex functions, and uses a sequential convex approximation algorithm, coupled with a Monte Carlo method, to solve the approximation. This approach is called a smooth Monte Carlo approach in this article. It is shown that the proposed approach is capable of handling both smooth and non-smooth JCCPs where the random variables can be either continuous, discrete, or mixed. The numerical experiments further confirm these findings.