Scenario-based cuts for structured two-stage stochastic and distributionally robust p-order conic mixed integer programs

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dc.contributor.authorBansal, Manishen
dc.contributor.authorZhang, Yingqiuen
dc.date.accessioned2022-02-13T16:26:41Zen
dc.date.available2022-02-13T16:26:41Zen
dc.date.issued2021-01-22en
dc.date.updated2022-02-13T16:26:39Zen
dc.description.abstractIn this paper, we derive (partial) convex hull for deterministic multi-constraint polyhedral conic mixed integer sets with multiple integer variables using conic mixed integer rounding (CMIR) cut-generation procedure of Atamtürk and Narayanan (Math Prog 122:1–20, 2008), thereby extending their result for a simple polyhedral conic mixed integer set with single constraint and one integer variable. We then introduce two-stage stochastic p-order conic mixed integer programs (denoted by TSS-CMIPs) in which the second stage problems have sum of lp-norms in the objective function along with integer variables. First, we present sufficient conditions under which the addition of scenario-based nonlinear cuts in the extensive formulation of TSS-CMIPs is sufficient to relax the integrality restrictions on the second stage integer variables without impacting the integrality of the optimal solution of the TSS-CMIP. We utilize scenario-based CMIR cuts for TSS-CMIPs and their distributionally robust generalizations with structured CMIPs in the second stage, and prove that these cuts provide conic/linear programming equivalent or approximation for the second stage CMIPs. We also perform extensive computational experiments by solving stochastic and distributionally robust capacitated facility location problem and randomly generated structured TSS-CMIPs with polyhedral CMIPs and second-order CMIPs in the second stage, i.e. p= 1 and p= 2 , respectively. We observe that there is a significant reduction in the total time taken to solve these problems after adding the scenario-based cuts.en
dc.description.versionAccepted versionen
dc.format.extentPages 391-433en
dc.format.extent43 page(s)en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1007/s10898-020-00986-wen
dc.identifier.eissn1573-2916en
dc.identifier.issn0925-5001en
dc.identifier.issue2en
dc.identifier.urihttp://hdl.handle.net/10919/108329en
dc.identifier.volume81en
dc.language.isoenen
dc.publisherSpringeren
dc.relation.urihttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000609400600001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=930d57c9ac61a043676db62af60056c1en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectOperations Research & Management Scienceen
dc.subjectMathematics, Applieden
dc.subjectMathematicsen
dc.subjectTwo-stage stochastic p-order conic mixed integer programen
dc.subjectScenario-based cutting planesen
dc.subjectTwo-stage distributionally robust programen
dc.subject(Partial) convex hullen
dc.subjectConic mixed integer roundingen
dc.subjectMulti-module capacitated facility locationen
dc.subjectINEQUALITIES FACETSen
dc.subjectVALID INEQUALITIESen
dc.subjectALGORITHMen
dc.subjectDECOMPOSITIONen
dc.subjectOPTIMIZATIONen
dc.subjectFORMULATIONSen
dc.subjectRECOURSEen
dc.subjectSETen
dc.subjectOperations Researchen
dc.subject0102 Applied Mathematicsen
dc.subject0103 Numerical and Computational Mathematicsen
dc.subject0802 Computation Theory and Mathematicsen
dc.titleScenario-based cuts for structured two-stage stochastic and distributionally robust p-order conic mixed integer programsen
dc.title.serialJournal of Global Optimizationen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten
dc.type.otherArticleen
dc.type.otherJournalen
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pubs.organisational-group/Virginia Tech/Engineering/Industrial and Systems Engineeringen
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