Sample quantile-based programming for non-convex separable chance constraints

We propose a sampling-based approximation to non-convex, separable, chance constrained optimization problems using sample quantiles. The proposed approach does not require any prior knowledge of the distribution or the moments of the uncertainty, and accommodates chance constraints that are non-convex in the decision variables. We prescribe the finite number of samples and the tightening necessary to produce a feasible solution to the original chance constrained optimization problem with bounded suboptimality. The proposed approximation has a low computational cost since the number of sample-based constraints does not grow with the number of samples, and the number of samples needed is independent of the number of decision variables. We show the effectiveness of the proposed solution in a stochastic motion planning problem with non-convex obstacle avoidance constraints.