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dc.contributor.authorKapelevich, Lea
dc.contributor.authorCoey, Chris
dc.contributor.authorVielma, Juan Pablo
dc.date.accessioned2022-06-13T18:27:39Z
dc.date.available2022-06-13T12:43:26Z
dc.date.available2022-06-13T18:27:39Z
dc.date.issued2022-06
dc.date.submitted2020-12
dc.identifier.issn0025-5610
dc.identifier.issn1436-4646
dc.identifier.urihttps://hdl.handle.net/1721.1/142960.2
dc.description.abstractAbstract Polynomial nonnegativity constraints can often be handled using the sum of squares condition. This can be efficiently enforced using semidefinite programming formulations, or as more recently proposed by Papp and Yildiz (Papp D in SIAM J O 29: 822–851, 2019), using the sum of squares cone directly in an interior point algorithm. Beyond nonnegativity, more complicated polynomial constraints (in particular, generalizations of the positive semidefinite, second order and $$\ell _1$$ ℓ 1 -norm cones) can also be modeled through structured sum of squares programs. We take a different approach and propose using more specialized cones instead. This can result in lower dimensional formulations, more efficient oracles for interior point methods, or self-concordant barriers with smaller parameters.en_US
dc.publisherSpringer Science and Business Media LLCen_US
dc.relation.isversionofhttps://doi.org/10.1007/s10107-022-01831-6en_US
dc.rightsCreative Commons Attributionen_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0en_US
dc.sourceSpringer Berlin Heidelbergen_US
dc.titleSum of squares generalizations for conic setsen_US
dc.typeArticleen_US
dc.identifier.citationKapelevich, Lea, Coey, Chris and Vielma, Juan P. 2022. "Sum of squares generalizations for conic sets."en_US
dc.contributor.departmentMassachusetts Institute of Technology. Operations Research Center
dc.contributor.departmentSloan School of Management
dc.relation.journalMathematical Programmingen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2022-06-12T03:25:49Z
dc.language.rfc3066en
dc.rights.holderThe Author(s)
dspace.embargo.termsN
dspace.date.submission2022-06-12T03:25:49Z
mit.licensePUBLISHER_CC
mit.metadata.statusAuthority Work Neededen_US


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