Academic Journal
Optimization over the Boolean Hypercube via Sums of Nonnegative Circuit Polynomials
| Τίτλος: | Optimization over the Boolean Hypercube via Sums of Nonnegative Circuit Polynomials |
|---|---|
| Συγγραφείς: | Dressler, Mareike, Kurpisz, Adam, de Wolff, Timo |
| Συνεισφορές: | Mareike Dressler and Adam Kurpisz and Timo de Wolff |
| Στοιχεία εκδότη: | Schloss Dagstuhl – Leibniz-Zentrum für Informatik |
| Έτος έκδοσης: | 2018 |
| Συλλογή: | DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) |
| Θεματικοί όροι: | nonnegativity certificate, hypercube optimization, sums of nonnegative circuit polynomials, relative entropy programming, sums of squares |
| Περιγραφή: | Various key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems are based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS based certificates remain valid: First, there exists a SONC certificate of degree at most n+d for polynomials which are nonnegative over the n-variate boolean hypercube with constraints of degree d. Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate, that includes at most n^O(d) nonnegative circuit polynomials. Finally, we show certain differences between SOS and SONC cones: we prove that, in contrast to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar's Positivestellensatz. We discuss these results both from algebraic and optimization perspective. |
| Τύπος εγγράφου: | article in journal/newspaper conference object |
| Περιγραφή αρχείου: | application/pdf |
| Γλώσσα: | English |
| Relation: | Is Part Of LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.82 |
| DOI: | 10.4230/LIPIcs.MFCS.2018.82 |
| Διαθεσιμότητα: | https://doi.org/10.4230/LIPIcs.MFCS.2018.82 https://nbn-resolving.org/urn:nbn:de:0030-drops-96643 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.82 |
| Rights: | https://creativecommons.org/licenses/by/3.0/legalcode |
| Αριθμός Καταχώρησης: | edsbas.4351E5AC |
| Βάση Δεδομένων: | BASE |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://doi.org/10.4230/LIPIcs.MFCS.2018.82# Name: EDS - BASE (ns324271) Category: fullText Text: View record from BASE |
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| Items | – Name: Title Label: Title Group: Ti Data: Optimization over the Boolean Hypercube via Sums of Nonnegative Circuit Polynomials – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Dressler%2C+Mareike%22">Dressler, Mareike</searchLink><br /><searchLink fieldCode="AR" term="%22Kurpisz%2C+Adam%22">Kurpisz, Adam</searchLink><br /><searchLink fieldCode="AR" term="%22de+Wolff%2C+Timo%22">de Wolff, Timo</searchLink> – Name: Author Label: Contributors Group: Au Data: Mareike Dressler and Adam Kurpisz and Timo de Wolff – Name: Publisher Label: Publisher Information Group: PubInfo Data: Schloss Dagstuhl – Leibniz-Zentrum für Informatik – Name: DatePubCY Label: Publication Year Group: Date Data: 2018 – Name: Subset Label: Collection Group: HoldingsInfo Data: DROPS - Dagstuhl Research Online Publication Server (Schloss Dagstuhl - Leibniz Center for Informatics ) – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22nonnegativity+certificate%22">nonnegativity certificate</searchLink><br /><searchLink fieldCode="DE" term="%22hypercube+optimization%22">hypercube optimization</searchLink><br /><searchLink fieldCode="DE" term="%22sums+of+nonnegative+circuit+polynomials%22">sums of nonnegative circuit polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22relative+entropy+programming%22">relative entropy programming</searchLink><br /><searchLink fieldCode="DE" term="%22sums+of+squares%22">sums of squares</searchLink> – Name: Abstract Label: Description Group: Ab Data: Various key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems are based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS based certificates remain valid: First, there exists a SONC certificate of degree at most n+d for polynomials which are nonnegative over the n-variate boolean hypercube with constraints of degree d. Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate, that includes at most n^O(d) nonnegative circuit polynomials. Finally, we show certain differences between SOS and SONC cones: we prove that, in contrast to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar's Positivestellensatz. We discuss these results both from algebraic and optimization perspective. – Name: TypeDocument Label: Document Type Group: TypDoc Data: article in journal/newspaper<br />conference object – Name: Format Label: File Description Group: SrcInfo Data: application/pdf – Name: Language Label: Language Group: Lang Data: English – Name: NoteTitleSource Label: Relation Group: SrcInfo Data: Is Part Of LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018); https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.82 – Name: DOI Label: DOI Group: ID Data: 10.4230/LIPIcs.MFCS.2018.82 – Name: URL Label: Availability Group: URL Data: https://doi.org/10.4230/LIPIcs.MFCS.2018.82<br />https://nbn-resolving.org/urn:nbn:de:0030-drops-96643<br />https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.82 – Name: Copyright Label: Rights Group: Cpyrght Data: https://creativecommons.org/licenses/by/3.0/legalcode – Name: AN Label: Accession Number Group: ID Data: edsbas.4351E5AC |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.4351E5AC |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.4230/LIPIcs.MFCS.2018.82 Languages: – Text: English Subjects: – SubjectFull: nonnegativity certificate Type: general – SubjectFull: hypercube optimization Type: general – SubjectFull: sums of nonnegative circuit polynomials Type: general – SubjectFull: relative entropy programming Type: general – SubjectFull: sums of squares Type: general Titles: – TitleFull: Optimization over the Boolean Hypercube via Sums of Nonnegative Circuit Polynomials Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Dressler, Mareike – PersonEntity: Name: NameFull: Kurpisz, Adam – PersonEntity: Name: NameFull: de Wolff, Timo – PersonEntity: Name: NameFull: Mareike Dressler and Adam Kurpisz and Timo de Wolff IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2018 Identifiers: – Type: issn-locals Value: edsbas – Type: issn-locals Value: edsbas.oa |
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