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. (C) 2019 ISA. Published by Elsevier Ltd. All rights reserved.