<?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-05184157</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="2026-05-24T21:40:37+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Regularization path via L0  Bregman relaxations</title>
            <author role="aut">
              <persName>
                <forename type="first">Mhamed</forename>
                <surname>Essafri</surname>
              </persName>
              <email type="md5">43ada8064561c9b41d1a13b19cba766e</email>
              <email type="domain">irit.fr</email>
              <idno type="idhal" notation="string">mhamed-essafri</idno>
              <idno type="idhal" notation="numeric">1436958</idno>
              <idno type="halauthorid" notation="string">3286399-1436958</idno>
              <idno type="ORCID">https://orcid.org/0009-0009-2695-4519</idno>
              <affiliation ref="#struct-1612880"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Luca</forename>
                <surname>Calatroni</surname>
              </persName>
              <email type="md5">7744c423d913bc229e1cd428648e9038</email>
              <email type="domain">i3s.unice.fr</email>
              <idno type="idhal" notation="string">luca-calatroni</idno>
              <idno type="idhal" notation="numeric">750125</idno>
              <idno type="halauthorid" notation="string">46527-750125</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-3887-1859</idno>
              <affiliation ref="#struct-204763"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Emmanuel</forename>
                <surname>Soubies</surname>
              </persName>
              <email type="md5">eb8448ce9a08c9f4fa3666ee6e87d5b6</email>
              <email type="domain">irit.fr</email>
              <idno type="idhal" notation="string">emmanuel-soubies</idno>
              <idno type="idhal" notation="numeric">225</idno>
              <idno type="halauthorid" notation="string">24119-225</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-0571-6983</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.com/citations?user=OouTPC0AAAAJ&amp;hl=fr</idno>
              <idno type="IDREF">https://www.idref.fr/198702949</idno>
              <affiliation ref="#struct-1612880"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Mhamed</forename>
                <surname>Essafri</surname>
              </persName>
              <email type="md5">43ada8064561c9b41d1a13b19cba766e</email>
              <email type="domain">irit.fr</email>
            </editor>
            <funder ref="#projanr-66000"/>
            <funder ref="#projeurop-753135"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2025-07-24 11:15:39</date>
              <date type="whenModified">2026-03-23 15:04:47</date>
              <date type="whenReleased">2025-07-24 13:58:02</date>
              <date type="whenProduced">2025-08-25</date>
              <date type="whenEndEmbargoed">2025-07-24</date>
              <ref type="file" target="https://hal.science/hal-05184157v1/document">
                <date notBefore="2025-07-24"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-05184157v1/file/l0Path_GRESTI_finalVersion.pdf" id="file-5184157-4469439">
                <date notBefore="2025-07-24"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="1465975">
                <persName>
                  <forename>Mhamed</forename>
                  <surname>Essafri</surname>
                </persName>
                <email type="md5">43ada8064561c9b41d1a13b19cba766e</email>
                <email type="domain">irit.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-05184157</idno>
            <idno type="halUri">https://hal.science/hal-05184157</idno>
            <idno type="halBibtex">essafri:hal-05184157</idno>
            <idno type="halRefHtml">&lt;i&gt;GRETSI&lt;/i&gt;, Aug 2025, Strasbourg, France</idno>
            <idno type="halRef">GRETSI, Aug 2025, Strasbourg, France</idno>
            <availability status="restricted">
              <licence target="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0 - Attribution<ref corresp="#file-5184157-4469439"/></licence>
            </availability>
          </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="OPENAIRE">OpenAIRE</idno>
            <idno type="stamp" n="UT1-CAPITOLE">Université Toulouse 1 Capitole</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="IRIT">IRIT - Institut de Recherche en Informatique de Toulouse</idno>
            <idno type="stamp" n="IRIT-SC" corresp="IRIT">Signal et Communications</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="IRIT-SI" corresp="IRIT">Signaux et Images</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="UT3-TOULOUSEINP">Université de Toulouse / Toulouse INP</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="3">National</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">Regularization path via L0  Bregman relaxations</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Mhamed</forename>
                    <surname>Essafri</surname>
                  </persName>
                  <email type="md5">43ada8064561c9b41d1a13b19cba766e</email>
                  <email type="domain">irit.fr</email>
                  <idno type="idhal" notation="string">mhamed-essafri</idno>
                  <idno type="idhal" notation="numeric">1436958</idno>
                  <idno type="halauthorid" notation="string">3286399-1436958</idno>
                  <idno type="ORCID">https://orcid.org/0009-0009-2695-4519</idno>
                  <affiliation ref="#struct-1612880"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Luca</forename>
                    <surname>Calatroni</surname>
                  </persName>
                  <email type="md5">7744c423d913bc229e1cd428648e9038</email>
                  <email type="domain">i3s.unice.fr</email>
                  <idno type="idhal" notation="string">luca-calatroni</idno>
                  <idno type="idhal" notation="numeric">750125</idno>
                  <idno type="halauthorid" notation="string">46527-750125</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-3887-1859</idno>
                  <affiliation ref="#struct-204763"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Emmanuel</forename>
                    <surname>Soubies</surname>
                  </persName>
                  <email type="md5">eb8448ce9a08c9f4fa3666ee6e87d5b6</email>
                  <email type="domain">irit.fr</email>
                  <idno type="idhal" notation="string">emmanuel-soubies</idno>
                  <idno type="idhal" notation="numeric">225</idno>
                  <idno type="halauthorid" notation="string">24119-225</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-0571-6983</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.com/citations?user=OouTPC0AAAAJ&amp;hl=fr</idno>
                  <idno type="IDREF">https://www.idref.fr/198702949</idno>
                  <affiliation ref="#struct-1612880"/>
                </author>
              </analytic>
              <monogr>
                <title level="m">GRETSI 2025</title>
                <meeting>
                  <title>GRETSI</title>
                  <date type="start">2025-08-25</date>
                  <date type="end">2025-08-29</date>
                  <settlement>Strasbourg</settlement>
                  <country key="FR">France</country>
                </meeting>
                <imprint/>
              </monogr>
              <ref type="publisher">https://gretsi.fr/colloque2025/</ref>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode>
              <classCode scheme="halDomain" n="info">Computer Science [cs]</classCode>
              <classCode scheme="halDomain" n="info.info-ts">Computer Science [cs]/Signal and Image Processing</classCode>
              <classCode scheme="halDomain" n="stat.ml">Statistics [stat]/Machine Learning [stat.ML]</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>The optimization of problems involving the L0-pseudo norm plays an important role in signal processing and machine learning. Due to the intrinsic NP-hardness of such problems, continuous (potentially non-convex) relaxations have gained significant attention in recent years. In particular, the notion of the L0 Bregman relaxations (B-rex)—a class of exact relaxations for L0-regularized criteria with general data terms defined in terms of Bregman distances—have been proposed. These relaxations are exact in the sense that they preserve global minimizers while eliminating certain local minimizers. Building on these properties, we propose a new algorithm to estimate the path of solutions across a range of sparsity levels. We discuss the methodological aspects of this approach, along with illustrative and numerical examples that demonstrate its effectiveness.</p>
            </abstract>
            <abstract xml:lang="fr">
              <p>L’optimisation des problèmes impliquant la pseudo-norme L0 joue un rôle important en traitement du signal et en apprentissage automatique. En raison de la nature intrinsèquement NP-difficile de ces problèmes, des relaxations continues (potentiellement non convexes) ont attiré une attention significative ces dernières années. En particulier, la notion de “L0 Bregman relaxation” (B-rex)—une classe de relaxations exactes pour des critères régularisés en norme L0 avec des termes d’attache aux données généraux définie à partir de distances de Bregman—a été proposée. Ces relaxations sont exactes dans le sens où elles préservent les minimiseurs globaux tout en éliminant certains minimiseurs locaux. En s’appuyant sur ces propriétés, nous proposons un nouvel algorithme pour estimer le chemin des solutions pour différents niveaux de parcimonie. Nous présentons les aspects méthodologiques de cette approche, ainsi que des exemples illustratifs et numériques démontrant son efficacité.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-1612880" status="VALID">
          <orgName>Signal et Communications</orgName>
          <orgName type="acronym">IRIT-SC</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>IRIT2 rue Charles Camichel 31071 Toulouse Cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.irit.fr/departement/signaux-images/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-1612872" type="direct"/>
            <relation active="#struct-81148" type="indirect"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="indirect"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation name="UMR5505" active="#struct-441569" type="indirect"/>
            <relation active="#struct-448187" type="indirect"/>
            <relation active="#struct-1574795" type="indirect"/>
            <relation active="#struct-1612865" type="indirect"/>
            <relation name="FED4171" active="#struct-1574795" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-204763" status="VALID">
          <orgName>Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova]</orgName>
          <orgName type="acronym">DIBRIS</orgName>
          <desc>
            <address>
              <addrLine>Via all'Opera Pia, 13 16145 Genova GE</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">http://www.dibris.unige.it/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-302889" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-1612872" status="VALID">
          <idno type="IdRef">030947448</idno>
          <idno type="ISNI">0000000121927225</idno>
          <idno type="RNSR">199511949P</idno>
          <idno type="ROR">https://ror.org/01rx4qw44</idno>
          <orgName>Institut de recherche en informatique de Toulouse</orgName>
          <orgName type="acronym">IRIT</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 Route de Narbonne, F-31062 Toulouse Cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.irit.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-81148" type="direct"/>
            <relation name="443875" active="#struct-443875" type="indirect"/>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation name="UMR5505" active="#struct-441569" type="direct"/>
            <relation active="#struct-448187" type="direct"/>
            <relation active="#struct-1574795" type="direct"/>
            <relation active="#struct-1612865" type="direct"/>
            <relation name="FED4171" active="#struct-1574795" 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-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="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>
        <org type="institution" xml:id="struct-1574795" status="VALID">
          <orgName>Université de Toulouse</orgName>
          <orgName type="acronym">EPE UT</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>118 toute de Narbonne, 31062 Toulouse cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-tlse3.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-443875" type="direct"/>
          </listRelation>
        </org>
        <org type="regrouplaboratory" xml:id="struct-1612865" status="VALID">
          <orgName>Toulouse Mind &amp; Brain Institut</orgName>
          <orgName type="acronym">TMBI</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>CHU Purpan, Pavillon Baudot, 31059 Toulouse cedex 9</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.tmbi.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-116256" type="direct"/>
            <relation active="#struct-443875" type="indirect"/>
            <relation name="FED4171" active="#struct-1574795" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-302889" status="VALID">
          <idno type="IdRef">032054262</idno>
          <idno type="ROR">https://ror.org/0107c5v14</idno>
          <idno type="Wikidata">032054262</idno>
          <orgName>Università degli studi di Genova = University of Genoa = Université de Gênes</orgName>
          <orgName type="acronym">UniGe</orgName>
          <desc>
            <address>
              <addrLine>Via Balbi, 5 - 16126 Genova</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">https://unige.it/it</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-66000" status="VALID">
          <idno type="anr">ANR-22-CE48-0004</idno>
          <orgName>EROSION</orgName>
          <desc>Relaxations exactes pour l'optimisation parcimonieuse et de faible rang</desc>
          <date type="start">2022</date>
        </org>
        <org type="europeanProject" xml:id="projeurop-753135" status="VALID">
          <idno type="number">101117133</idno>
          <idno type="program">ERC-2023-STG</idno>
          <idno type="call">ERC-2023-STG</idno>
          <orgName>MALIN</orgName>
          <desc>Model-aware learning for imaging inverse problems in fluorescence microscopy</desc>
          <date type="start">2024-11-01</date>
          <date type="end">2029-10-31</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>