Mathematical programs with distributionally robust chance constraints: Statistical robustness, discretization and reformulation

In this paper, we consider mathematical programs with distributionally robust chance constraints (MPDRCC), where the ambiguity set is given by the general moment information. From the contaminated data-driven viewpoint, we first study the qualitative statistical robustness of MPDRCC. Then, motivated by the computational tractability, we investigate the discrete approximation of MPDRCC. The corresponding convergence results of the optimal value and the optimal solution set of the discrete approximation problem are established. After that, a reformulation of the discrete approximation problem is presented under standard assumptions, which is applied to solve MPDRCC approximately according to the above convergence results. Finally, two applications are reported, and some numerical results show that the statistical robustness assertion and the discrete approximation scheme are practical and effective.

Automated summary

This paper discusses mathematical programs with distributionally robust chance constraints (MPDRCC), where the ambiguity set is determined by general moment information. The qualitative statistical robustness of MPDRCC is studied from the contaminated data-driven viewpoint. Discrete approximation of MPDRCC is also investigated to achieve computational tractability, with established convergence results. A reformulation of the approximated problem under standard assumptions is presented, which is then applied to approximately solve MPDRCC based on the convergence results. Two applications are reported, showing the practicality and effectiveness of the statistical robustness assertion and the discrete approximation scheme.