Consistency of Distributionally Robust Risk- and Chance-Constrained Optimization Under Wasserstein Ambiguity Sets | IEEE Journals & Magazine | IEEE Xplore

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


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 c...Show More

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.
Published in: IEEE Control Systems Letters ( Volume: 5, Issue: 5, November 2021)
Page(s): 1729 - 1734
Date of Publication: 08 December 2020
Electronic ISSN: 2475-1456

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