Show simple item record

dc.contributor.authorDostert, Maria
dc.contributor.authorde Laat, David
dc.contributor.authorMoustrou, Philippe
dc.date.accessioned2022-03-24T09:38:37Z
dc.date.available2022-03-24T09:38:37Z
dc.date.issued2021-05-25
dc.description.abstractIn this paper we give an algorithm to round the floating point output of a semidefinite programming solver to a solution over the rationals or a quadratic extension of the rationals. This algorithm does not require the solution to be strictly feasible and works for large problems. We apply this to get sharp bounds for packing problems, and we use these sharp bounds to prove that certain optimal packing configurations are unique up to rotations. In particular, we show that the configuration coming from the E<sub>8</sub> root lattice is the unique optimal code with minimal angular distance π/3 on the hemisphere in R<sup>8</sup> , and we prove that the three-point bound for the (3, 8, ϑ)-spherical code, where ϑ is such that cos ϑ = (2√ 2 − 1)/7, is sharp by rounding to Q[ √ 2]. We also use our machinery to compute sharp upper bounds on the number of spheres that can be packed into a larger sphere.en_US
dc.identifier.citationDostert, de Laat, Moustrou. Exact semidefinite programming bounds for packing problems. SIAM Journal on Optimization. 2021;31(2):1433-1458en_US
dc.identifier.cristinIDFRIDAID 2006908
dc.identifier.doi10.1137/20M1351692
dc.identifier.issn1052-6234
dc.identifier.issn1095-7189
dc.identifier.urihttps://hdl.handle.net/10037/24531
dc.language.isoengen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.journalSIAM Journal on Optimization
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2021 Society for Industrial and Applied Mathematicsen_US
dc.titleExact semidefinite programming bounds for packing problemsen_US
dc.type.versionacceptedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


File(s) in this item

Thumbnail

This item appears in the following collection(s)

Show simple item record