A MCMC/Bernstein Approach to Chance Constrained Programs

This paper presents an extension of convex Bernstein approximations to non-affine and dependent chance constrained optimization problems. The Bernstein approximation technique transcribes probabilistic constraints into conservative convex deterministic constraints, relying heavily upon the evaluation of exponential moment generating functions. This is a computationally burdensome task for non-affine probabilistic constraints involving dependent random variables. In this paper, the theoretical framework of Bernstein approximations is combined with the practical benefits of Markov chain Monte Carlo (MCMC) integration for its use in a range of high dimensional applications. Numerical results for the combined Bernstein/MCMC approach are compared with scenario approximations.