Consistency of Distributionally Robust Risk-and Chance-Constrained Optimization under Wasserstein Ambiguity Sets

Ashish Cherukuri, Ashish R. Hota

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Abstract

We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where the constraints are required to hold for a family of distributions constructed from the observed realizations of the uncertainty via the Wasserstein distance. Our main results establish that if the samples are drawn independently from an underlying distribution and the problems satisfy suitable technical assumptions, then the optimal value and optimizers of the distributionally robust versions of these problems converge to the respective quantities of the original problems, as the sample size increases.

Original languageEnglish
Pages (from-to)1729-1734
Number of pages6
JournalIEEE Control Systems Letters
Volume5
Issue number5
Early online date8-Dec-2020
DOIs
Publication statusPublished - Nov-2021

Keywords

  • Optimization
  • stochastic systems.

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