On Distributionally Robust Chance Constrained Program with Wasserstein Distance

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dc.contributor.authorXie, W.en
dc.contributor.departmentIndustrial and Systems Engineeringen
dc.date.accessioned2018-07-25T20:44:20Zen
dc.date.available2018-07-25T20:44:20Zen
dc.date.issued2018-06-21en
dc.description.abstractThis paper studies a distributionally robust chance constrained program (DRCCP) with Wasserstein ambiguity set, where the uncertain constraints should satisfy with a probability at least a given threshold for all the probability distributions of the uncertain parameters within a chosen Wasserstein distance from an empirical distribution. In this work, we investigate equivalent reformulations and approximations of such problems. We first show that a DRCCP can be reformulated as a conditional-value-at-risk constrained optimization problem, and thus admits tight inner and outer approximations. When the metric space of uncertain parameters is a normed vector space, we show that a DRCCP of bounded feasible region is mixed integer representable by introducing big-M coefficients and additional binary variables. For a DRCCP with pure binary decision variables, by exploring submodular structure, we show that it admits a big-M free formulation and can be solved by branch and cut algorithm. This result can be generalized to mixed integer DRCCPs. Finally, we present a numerical study to illustrate effectiveness of the proposed methods.en
dc.description.notes28 pagesen
dc.format.mimetypeapplication/pdfen
dc.identifier.orcidXie, W [0000-0001-5157-1194]en
dc.identifier.urihttp://hdl.handle.net/10919/84391en
dc.language.isoenen
dc.relation.urihttp://arxiv.org/abs/1806.07418v1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectmath.OCen
dc.subject90C15, 90C22, 90C59en
dc.titleOn Distributionally Robust Chance Constrained Program with Wasserstein Distanceen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
pubs.organisational-group/Virginia Techen
pubs.organisational-group/Virginia Tech/All T&R Facultyen
pubs.organisational-group/Virginia Tech/Engineeringen
pubs.organisational-group/Virginia Tech/Engineering/COE T&R Facultyen
pubs.organisational-group/Virginia Tech/Engineering/Industrial and Systems Engineeringen

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