Distributionally robust chance constrained problem under interval distribution information
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This paper is concerned with distributionally robust chance constrained problem under interval distribution information. Using worst-case CVaR approximation, we present a tractable convex programming approximation for distributionally robust individual chance constrained problem under interval sets of mean and covariance information. We prove the worst-case CVaR approximation problem is an exact form of the distributionally robust individual chance constrained problem. Then, our result is applied to worst-case Value-at-Risk optimization problem. Moreover, we discuss the problem under several ambiguous distribution information and investigate tractable approximations for distributionally robust joint chance constrained problem. Finally, we provide an illustrative example to show our results.
KeywordsRobust optimization Chance constraint Interval distribution information Convex programming
The authors are grateful to the editor and the referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (11471230, 11671282).