<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04440949</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-15T07:25:52+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Upper bound hierarchies for noncommutative polynomial optimization</title>
            <author role="aut">
              <persName>
                <forename type="first">Igor</forename>
                <surname>Klep</surname>
              </persName>
              <idno type="halauthorid">338814-0</idno>
              <affiliation ref="#struct-38374"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Victor</forename>
                <surname>Magron</surname>
              </persName>
              <email type="md5">e6a7b2d612c489f5e1b7c534a60cc52f</email>
              <email type="domain">laas.fr</email>
              <idno type="idhal" notation="string">victor-magron</idno>
              <idno type="idhal" notation="numeric">171112</idno>
              <idno type="halauthorid" notation="string">20340-171112</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-1147-3738</idno>
              <idno type="IDREF">https://www.idref.fr/176992316</idno>
              <affiliation ref="#struct-1099620"/>
              <affiliation ref="#struct-1954"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Gaël</forename>
                <surname>Massé</surname>
              </persName>
              <idno type="halauthorid">2119243-0</idno>
              <affiliation ref="#struct-1099620"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jurij</forename>
                <surname>Volčič</surname>
              </persName>
              <idno type="halauthorid">1989673-0</idno>
              <affiliation ref="#struct-11333"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Victor</forename>
                <surname>Magron</surname>
              </persName>
              <email type="md5">e6a7b2d612c489f5e1b7c534a60cc52f</email>
              <email type="domain">laas.fr</email>
            </editor>
            <funder ref="#projanr-49786"/>
            <funder ref="#projeurop-721721"/>
            <funder>This work was supported by the Slovenian Research Agency program P1-0222 and grants J1-50002, J1-2453, N1-0217, J1-3004, the NSF grant DMS-1954709, the FastQI grant funded bythe Institut Quantique Occitan, the HORIZON–MSCA-2023-DNJD of the European Commission under the Grant Agreement No 101120296 (TENORS)</funder>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2024-02-06 11:26:31</date>
              <date type="whenModified">2026-02-17 14:14:01</date>
              <date type="whenReleased">2024-02-06 11:26:31</date>
              <date type="whenProduced">2024-08-19</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/2402.02126"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="189461">
                <persName>
                  <forename>Victor</forename>
                  <surname>Magron</surname>
                </persName>
                <email type="md5">e6a7b2d612c489f5e1b7c534a60cc52f</email>
                <email type="domain">laas.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04440949</idno>
            <idno type="halUri">https://laas.hal.science/hal-04440949</idno>
            <idno type="halBibtex">klep:hal-04440949</idno>
            <idno type="halRefHtml">&lt;i&gt;26th International Symposium on Mathematical Theory of Networks and Systems (MTNS)&lt;/i&gt;, Aug 2024, Cambridge (Angleterre), United Kingdom</idno>
            <idno type="halRef">26th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Aug 2024, Cambridge (Angleterre), United Kingdom</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-TLSE2">Université Toulouse 2</idno>
            <idno type="stamp" n="UNIV-TLSE3">Université de Toulouse</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSA-TOULOUSE">Institut National des Sciences Appliquées de Toulouse</idno>
            <idno type="stamp" n="LAAS">Laboratoire d'analyse et d'architecture des systèmes</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="OPENAIRE">OpenAIRE</idno>
            <idno type="stamp" n="IMT">Institut de Mathématiques de Toulouse</idno>
            <idno type="stamp" n="UT1-CAPITOLE">Université Toulouse 1 Capitole</idno>
            <idno type="stamp" n="LAAS-DECISION-ET-OPTIMISATION" corresp="LAAS">LAAS-Décision et Optimisation</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="CIMI-TOULOUSE">Centre International de Mathématiques et d'Informatique de Toulouse</idno>
            <idno type="stamp" n="TOULOUSE-INP">Toulouse - INP</idno>
            <idno type="stamp" n="UNIV-UT3">Université Toulouse 3</idno>
            <idno type="stamp" n="UT3-INP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="LAAS-POP" corresp="LAAS-DECISION-ET-OPTIMISATION">Polynomial OPtimization</idno>
            <idno type="stamp" n="UT3-TOULOUSEINP">Université de Toulouse / Toulouse INP</idno>
            <idno type="stamp" n="TEST7-HALCNRS">test 7 du portail hal cnrs</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">4 pages</note>
            <note type="audience" n="2">International</note>
            <note type="invited" n="0">No</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
            <note type="proceedings" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Upper bound hierarchies for noncommutative polynomial optimization</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Igor</forename>
                    <surname>Klep</surname>
                  </persName>
                  <idno type="halauthorid">338814-0</idno>
                  <affiliation ref="#struct-38374"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Victor</forename>
                    <surname>Magron</surname>
                  </persName>
                  <email type="md5">e6a7b2d612c489f5e1b7c534a60cc52f</email>
                  <email type="domain">laas.fr</email>
                  <idno type="idhal" notation="string">victor-magron</idno>
                  <idno type="idhal" notation="numeric">171112</idno>
                  <idno type="halauthorid" notation="string">20340-171112</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-1147-3738</idno>
                  <idno type="IDREF">https://www.idref.fr/176992316</idno>
                  <affiliation ref="#struct-1099620"/>
                  <affiliation ref="#struct-1954"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Gaël</forename>
                    <surname>Massé</surname>
                  </persName>
                  <idno type="halauthorid">2119243-0</idno>
                  <affiliation ref="#struct-1099620"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jurij</forename>
                    <surname>Volčič</surname>
                  </persName>
                  <idno type="halauthorid">1989673-0</idno>
                  <affiliation ref="#struct-11333"/>
                </author>
              </analytic>
              <monogr>
                <idno type="localRef">Rapport LAAS n° 24088</idno>
                <title level="m">Proceedings of the 26th International Symposium on Mathematical Theory of Networks and Systems (MTNS)</title>
                <meeting>
                  <title>26th International Symposium on Mathematical Theory of Networks and Systems (MTNS)</title>
                  <date type="start">2024-08-19</date>
                  <date type="end">2024-08-23</date>
                  <settlement>Cambridge (Angleterre)</settlement>
                  <country key="GB">United Kingdom</country>
                </meeting>
                <imprint>
                  <date type="datePub">2024-02-03</date>
                </imprint>
              </monogr>
              <idno type="arxiv">2402.02126</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="classification">90C22, 90C26</classCode>
              <classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode>
              <classCode scheme="halDomain" n="math.math-fa">Mathematics [math]/Functional Analysis [math.FA]</classCode>
              <classCode scheme="halDomain" n="phys.qphy">Physics [physics]/Quantum Physics [quant-ph]</classCode>
              <classCode scheme="halTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halOldTypology" n="COMM">Conference papers</classCode>
              <classCode scheme="halTreeTypology" n="COMM">Conference papers</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>This work focuses on minimizing the eigenvalue of a noncommutative polynomial subject to a finite number of noncommutative polynomial inequality constraints. Based on the Helton-McCullough Positivstellensatz, the noncommutative analog of Lasserre's moment-sum of squares hierarchy provides a sequence of lower bounds converging to the minimal eigenvalue, under mild assumptions on the constraint set. Each lower bound can be obtained by solving a semidefinite program. We derive complementary converging hierarchies of upper bounds. They are noncommutative analogues of the upper bound hierarchies due to Lasserre for minimizing polynomials over compact sets. Each upper bound can be obtained by solving a generalized eigenvalue problem.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="regrouplaboratory" xml:id="struct-38374" status="VALID">
          <orgName>Faculty of Mathematics and Physics [Ljubljana]</orgName>
          <orgName type="acronym">UL | FMF</orgName>
          <date type="start">1995-01-01</date>
          <desc>
            <address>
              <addrLine>University of Ljubljana | Jadranska ulica 19, 1000 Ljubljana</addrLine>
              <country key="SI"/>
            </address>
            <ref type="url">https://www.fmf.uni-lj.si/en/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-302844" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-1099620" status="OLD">
          <orgName>Equipe Polynomial OPtimization</orgName>
          <orgName type="acronym">LAAS-POP</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://hal.laas.fr/LAAS-POP/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-459" type="direct"/>
            <relation active="#struct-81148" type="indirect"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="indirect"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="indirect"/>
            <relation active="#struct-217752" type="indirect"/>
            <relation name="UPR8001" active="#struct-441569" type="indirect"/>
            <relation active="#struct-448187" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1954" status="OLD">
          <idno type="IdRef">166783900</idno>
          <idno type="ISNI">0000000403836348</idno>
          <idno type="RNSR">200711888W</idno>
          <idno type="ROR">https://ror.org/014vp6c30</idno>
          <orgName>Institut de Mathématiques de Toulouse UMR5219</orgName>
          <orgName type="acronym">IMT</orgName>
          <date type="start">2007-01-01</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>UPS IMT, F-31062 Toulouse Cedex 9, INSA Toulouse, F-31077 Toulouse,France UT1, F-31042 Toulouse, France UT2, F-31058 Toulouse,Téléphone : 05.61.55.67.90</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.math.univ-toulouse.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-217752" type="direct"/>
            <relation name="UMR5219" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-11333" status="VALID">
          <idno type="ROR">https://ror.org/04bdffz58</idno>
          <orgName>Drexel University</orgName>
          <desc>
            <address>
              <addrLine>3141 Chestnut Street, Philadelphia, PA 19104</addrLine>
              <country key="US"/>
            </address>
            <ref type="url">http://www.drexel.edu/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-302844" status="VALID">
          <idno type="ROR">https://ror.org/05njb9z20</idno>
          <orgName>University of Ljubljana</orgName>
          <desc>
            <address>
              <addrLine>Kongresni trg 12, 1000 Ljubljana</addrLine>
              <country key="SI"/>
            </address>
            <ref type="url">https://www.uni-lj.si/eng/</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-459" status="OLD">
          <idno type="IdRef">199278792</idno>
          <idno type="ISNI">0000 0001 2188 216X </idno>
          <idno type="RNSR">199517454Y</idno>
          <idno type="ROR">https://ror.org/03vcm6439</idno>
          <orgName>Laboratoire d'analyse et d'architecture des systèmes</orgName>
          <orgName type="acronym">LAAS</orgName>
          <date type="start">1968-01-01</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>7 Av du colonel Roche 31077 TOULOUSE CEDEX 4</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.laas.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116255" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-217752" type="direct"/>
            <relation name="UPR8001" active="#struct-441569" type="direct"/>
            <relation active="#struct-448187" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-81148" status="VALID">
          <idno type="IdRef">026404354</idno>
          <idno type="ISNI">0000000121902837</idno>
          <idno type="ROR">https://ror.org/0443n9e75</idno>
          <orgName>Université Toulouse Capitole</orgName>
          <orgName type="acronym">UT Capitole</orgName>
          <date type="start">1970-01-01</date>
          <desc>
            <address>
              <addrLine>2 rue du Doyen-Gabriel-Marty - 31042 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ut-capitole.fr/</ref>
          </desc>
          <listRelation>
            <relation name="443875" active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-443875" status="VALID">
          <idno type="ROR">https://ror.org/017tgbk05</idno>
          <orgName>Communauté d'universités et établissements de Toulouse</orgName>
          <orgName type="acronym">Comue de Toulouse</orgName>
          <desc>
            <address>
              <addrLine>41 Allée Jules Guesde, 31000 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-toulouse.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116255" status="VALID">
          <idno type="IdRef">026388766</idno>
          <idno type="ISNI">0000 0001 2286 8343</idno>
          <idno type="ROR">https://ror.org/01h8pf755</idno>
          <idno type="Wikidata">Q858979</idno>
          <orgName>Institut National des Sciences Appliquées - Toulouse</orgName>
          <orgName type="acronym">INSA Toulouse</orgName>
          <date type="start">1963-10-21</date>
          <desc>
            <address>
              <addrLine>135, avenue de Rangueil - 31077 Toulouse cedex 4</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-toulouse.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301232" type="direct"/>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-116256" status="VALID">
          <idno type="IdRef">026403994</idno>
          <idno type="ROR">https://ror.org/04ezk3x31</idno>
          <orgName>Université Toulouse - Jean Jaurès</orgName>
          <orgName type="acronym">UT2J</orgName>
          <date type="start">1971-01-01</date>
          <desc>
            <address>
              <addrLine>5 allées Antonio Machado - 31058 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse2.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-217752" status="OLD">
          <idno type="IdRef">026404672</idno>
          <idno type="ISNI">0000000121617331</idno>
          <idno type="ROR">https://ror.org/02v6kpv12</idno>
          <idno type="Wikidata">Q1273188</idno>
          <orgName>Université Toulouse III - Paul Sabatier</orgName>
          <orgName type="acronym">UT3</orgName>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 route de Narbonne - 31062 Toulouse</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-tlse3.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-448187" status="VALID">
          <idno type="IdRef">026388820</idno>
          <idno type="ISNI">0000000121766169</idno>
          <idno type="ROR">https://ror.org/033p9g875</idno>
          <orgName>Institut National Polytechnique (Toulouse)</orgName>
          <orgName type="acronym">Toulouse INP</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.inp-toulouse.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-49786" status="VALID">
          <idno type="anr">ANR-11-LABX-0040</idno>
          <orgName>CIMI</orgName>
          <desc>Centre International de Mathématiques et d'Informatique (de Toulouse)</desc>
          <date type="start">2011</date>
        </org>
        <org type="europeanProject" xml:id="projeurop-721721" status="VALID">
          <idno type="number">101017733</idno>
          <idno type="program">H2020-FETFLAG-2018-2020</idno>
          <idno type="call">H2020-FETFLAG-2020-02</idno>
          <orgName>QuantERA II</orgName>
          <desc>QuantERA II ERA-NET Cofund in Quantum Technologies</desc>
          <date type="start">2021-01-01</date>
          <date type="end">2026-12-31</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>