Robust Optimization Model for a Class of Uncertain Linear Programs

In the paper, we propose a tractable robust counterpart for solving the uncertain linear optimization problem with correlated uncertainties related to a causal ARMA(p, q) process. This explicit treatment of correlated uncertainties under a time series setting in robust optimization is in contrast to the independent or simple correlated uncertainties assumption in existing literature. under some reasonable assumptions, we establish probabilistic guarantees for the feasibility of the robust solution. Finally, we provide a numerical method for the selection of the parameters which controls the tradeoff among the tractability, the robustness and the optimality of the robust model.