## Abstract

We present a data-driven approach for distri-butionally robust chance constrained optimization problems (DRCCPs). We consider the case where the decision maker has access to a finite number of samples or realizations of the uncertainty. The chance constraint is then required to hold for all distributions that are close to the empirical distribution constructed from the samples (where the distance between two distributions is defined via the Wasserstein metric). We first reformulate DRCCPs under data-driven Wasserstein ambiguity sets and a general class of constraint functions. When the feasibility set of the chance constraint program is replaced by its convex inner approximation, we present a convex reformulation of the program and show its tractability when the constraint function is affine in both the decision variable and the uncertainty. For constraint functions concave in the uncertainty, we show that a cutting-surface algorithm converges to an approximate solution of the convex inner approximation of DRCCPs. Finally, for constraint functions convex in the uncertainty, we compare the feasibility set with other sample-based approaches for chance constrained programs.

Original language | English |
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Title of host publication | Proceedings of the American Control Conference, ACC 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Chapter | 8814677 |

Pages | 1501-1506 |

Number of pages | 6 |

ISBN (Electronic) | 9781538679265 |

Publication status | Published - 1-Jul-2019 |

Event | 2019 American Control Conference, ACC 2019 - Philadelphia, United States Duration: 10-Jul-2019 → 12-Jul-2019 |

### Conference

Conference | 2019 American Control Conference, ACC 2019 |
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Country/Territory | United States |

City | Philadelphia |

Period | 10/07/2019 → 12/07/2019 |