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dc.contributor.authorFawzi, Hamza
dc.contributor.authorSaunderson, James F
dc.contributor.authorParrilo, Pablo A.
dc.date.accessioned2019-07-09T14:09:33Z
dc.date.available2019-07-09T14:09:33Z
dc.date.submitted2014-09
dc.identifier.issn0364-765X
dc.identifier.urihttps://hdl.handle.net/1721.1/121531
dc.description.abstractGiven a polytope P n , we say that P has a positive semidefinite lift (psd lift) of size d if one can express P as the projection of an affine slice of the d×d positive semidefinite cone. Such a representation allows us to solve linear optimization problems over P using a semidefinite program of size d and can be useful in practice when d is much smaller than the number of facets of P. If a polytope P has symmetry, we can consider equivariant psd lifts, i.e., those psd lifts that respect the symmetries of P. One of the simplest families of polytopes with interesting symmetries is regular polygons in the plane. In this paper, we give tight lower and upper bounds on the size of equivariant psd lifts for regular polygons. We give an explicit construction of an equivariant psd lift of the regular 2n-gon of size 2n - 1, and we prove that our construction is essentially optimal by proving a lower bound on the size of any equivariant psd lift of the regular N-gon that is logarithmic in N. Our construction is exponentially smaller than the (equivariant) psd lift obtained from the Lasserre/sum-of-squares hierarchy, and it also gives the first example of a polytope with an exponential gap between equivariant psd lifts and equivariant linear programming lifts. Finally we prove that our construction is essentially optimal by showing that any equivariant psd lift of the regular N-gon must have size at least logarithmic in N.en_US
dc.language.isoen
dc.publisherInstitute for Operations Research and the Management Sciences (INFORMS)en_US
dc.relation.isversionof10.1287/MOOR.2016.0813en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleEquivariant Semidefinite Lifts of Regular Polygonsen_US
dc.typeArticleen_US
dc.identifier.citationFawzi, Hamza, James Saunderson and Pablo A. Parrilo. "Equivariant semidefinite lifts of regular polygons." Mathematics of Operations Research 42, no. 2 (2016): 472-494.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.contributor.departmentMassachusetts Institute of Technology. Laboratory for Information and Decision Systemsen_US
dc.relation.journalMathematics of Operations Researchen_US
dc.eprint.versionOriginal manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/NonPeerRevieweden_US
dc.date.updated2019-06-28T18:41:23Z
dspace.date.submission2019-06-28T18:41:24Z
mit.journal.volume42en_US
mit.journal.issue2en_US


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