Global optimization of robust chance constrained problems
Journal of Global Optimization
On Safe Tractable Approximations of Chance-Constrained Linear Matrix Inequalities
Mathematics of Operations Research
Constructing Risk Measures from Uncertainty Sets
Operations Research
Solving chance-constrained combinatorial problems to optimality
Computational Optimization and Applications
A Soft Robust Model for Optimization Under Ambiguity
Operations Research
A relaxation algorithm with a probabilistic guarantee for robust deviation optimization
Computational Optimization and Applications
Theory and Applications of Robust Optimization
SIAM Review
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Robust Storage Assignment in Unit-Load Warehouses
Management Science
Randomized sampling for large zero-sum games
Automatica (Journal of IFAC)
Safe Approximations of Ambiguous Chance Constraints Using Historical Data
INFORMS Journal on Computing
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In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set ** of the distributions is of the form ** where ρp denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled problem where each constraint is a robust constraint centered at a sample drawn according to the central measure **. The main contribution of this paper is to show that the robust sampled problem is a good approximation for the ambiguous chance constrained problem with a high probability. This result is established using the Strassen-Dudley Representation Theorem that states that when the distributions of two random variables are close in the Prohorov metric one can construct a coupling of the random variables such that the samples are close with a high probability. We also show that the robust sampled problem can be solved efficiently both in theory and in practice.