Chance-constrained optimization for nonconvex programs using scenario-based methods

This paper presents a scenario-based method to solve the chance-constrained optimization for the nonconvex program. The sample complexity is first developed to guarantee the probabilistic feasibility. Then through the sampling on uncertain parameters, many scenarios are generated to form a large-scale deterministic approximation for the original chance-constrained program. Solving the resulting scenario-based nonconvex optimization is usually time-consuming. To overcome this challenge, we propose a sequential approach to find the global optimum more efficiently. Moreover, two novel schemes: branching-and-sampling and branching-and-discarding are developed for the chance-constrained 0-1 program by refining the scenario set in order to find a less conservative solution. Finally, model predictive control and process scheduling problem are taken as examples to evaluate the effectiveness of proposed optimization approaches.