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

Jie Jiang and Shen Peng

European Journal of Operational Research, 2024, vol. 313, issue 2, 616-627

Abstract: 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.

Keywords: Stochastic programming; Chance constrained optimization; Distributional robustness; Statistical robustness; Discretization (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:313:y:2024:i:2:p:616-627

DOI: 10.1016/j.ejor.2023.10.020

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