<?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-04821125</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="2026-05-02T06:23:44+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N&amp;lt;= 3$$</title>
            <author role="co_first_author">
              <persName>
                <forename type="first">Cyrille</forename>
                <surname>Kenne</surname>
              </persName>
              <idno type="halauthorid">44352-0</idno>
              <affiliation ref="#struct-366034"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Gisèle</forename>
                <surname>Mophou</surname>
              </persName>
              <email type="md5">5c299f4398256aef24c774855cacdaba</email>
              <email type="domain">univ-antilles.fr</email>
              <idno type="idhal" notation="string">gisele-mophou-loudjom</idno>
              <idno type="idhal" notation="numeric">11959</idno>
              <idno type="halauthorid" notation="string">33546-11959</idno>
              <idno type="ORCID">https://orcid.org/0000-0001-7949-8152</idno>
              <idno type="IDREF">https://www.idref.fr/174652887</idno>
              <affiliation ref="#struct-527183"/>
            </author>
            <author role="crp">
              <persName>
                <forename type="first">Mahamadi</forename>
                <surname>Warma</surname>
              </persName>
              <email type="md5">c7330070c5ca062c457aea4c535d9c10</email>
              <email type="domain">upr.edu</email>
              <idno type="idhal" notation="string">mahamadi-warma</idno>
              <idno type="idhal" notation="numeric">17878</idno>
              <idno type="halauthorid" notation="string">29031-17878</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-2342-9585</idno>
              <affiliation ref="#struct-303239"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>GISELE</forename>
                <surname>MOPHOU LOUDJOM</surname>
              </persName>
              <email type="md5">5c299f4398256aef24c774855cacdaba</email>
              <email type="domain">univ-antilles.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2024-12-05 15:48:54</date>
              <date type="whenModified">2026-04-14 13:54:02</date>
              <date type="whenReleased">2024-12-05 15:48:54</date>
              <date type="whenProduced">2024-12-04</date>
              <ref type="externalLink" target="https://link.springer.com/content/pdf/10.1007/s13540-024-00359-0.pdf"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="486527">
                <persName>
                  <forename>GISELE</forename>
                  <surname>MOPHOU LOUDJOM</surname>
                </persName>
                <email type="md5">5c299f4398256aef24c774855cacdaba</email>
                <email type="domain">univ-antilles.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04821125</idno>
            <idno type="halUri">https://hal.science/hal-04821125</idno>
            <idno type="halBibtex">kenne:hal-04821125</idno>
            <idno type="halRefHtml">&lt;i&gt;Fractional Calculus and Applied Analysis&lt;/i&gt;, 2024, &lt;a target="_blank" href="https://dx.doi.org/10.1007/s13540-024-00359-0"&gt;&amp;#x27E8;10.1007/s13540-024-00359-0&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Fractional Calculus and Applied Analysis, 2024, &amp;#x27E8;10.1007/s13540-024-00359-0&amp;#x27E9;</idno>
            <availability status="restricted"/>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-AG">Université des Antilles</idno>
            <idno type="stamp" n="BNRMI" corresp="UNIV-AG">Bibliothèque Numérique de Recherche en Mathématiques et Informatique</idno>
            <idno type="stamp" n="LAMIA" corresp="UNIV-AG">LAboratoire de Mathématiques Informatique et Applications [UR1_1]</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension $$N&amp;lt;= 3$$</title>
                <author role="co_first_author">
                  <persName>
                    <forename type="first">Cyrille</forename>
                    <surname>Kenne</surname>
                  </persName>
                  <idno type="halauthorid">44352-0</idno>
                  <affiliation ref="#struct-366034"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Gisèle</forename>
                    <surname>Mophou</surname>
                  </persName>
                  <email type="md5">5c299f4398256aef24c774855cacdaba</email>
                  <email type="domain">univ-antilles.fr</email>
                  <idno type="idhal" notation="string">gisele-mophou-loudjom</idno>
                  <idno type="idhal" notation="numeric">11959</idno>
                  <idno type="halauthorid" notation="string">33546-11959</idno>
                  <idno type="ORCID">https://orcid.org/0000-0001-7949-8152</idno>
                  <idno type="IDREF">https://www.idref.fr/174652887</idno>
                  <affiliation ref="#struct-527183"/>
                </author>
                <author role="crp">
                  <persName>
                    <forename type="first">Mahamadi</forename>
                    <surname>Warma</surname>
                  </persName>
                  <email type="md5">c7330070c5ca062c457aea4c535d9c10</email>
                  <email type="domain">upr.edu</email>
                  <idno type="idhal" notation="string">mahamadi-warma</idno>
                  <idno type="idhal" notation="numeric">17878</idno>
                  <idno type="halauthorid" notation="string">29031-17878</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-2342-9585</idno>
                  <affiliation ref="#struct-303239"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">124290</idno>
                <idno type="issn">1311-0454</idno>
                <title level="j">Fractional Calculus and Applied Analysis</title>
                <imprint>
                  <publisher>De Gruyter</publisher>
                  <date type="datePub">2024-12-04</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1007/s13540-024-00359-0</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Nonlinear fractional equation Nonlinear fractional equation</term>
                <term xml:lang="en">non-smooth optimization</term>
                <term xml:lang="en">strongstationarity</term>
                <term xml:lang="en">optimal solutions</term>
              </keywords>
              <classCode scheme="halDomain" n="math">Mathematics [math]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Abstract In this paper, we investigate the optimal control of a semi-linear fractional PDEs involving the spectral diffusion operator, or the realization of the integral fractional Laplace operator with the zero Dirichlet exterior condition, both of order s with $$s\in (0,1)$$ s ∈ ( 0 , 1 ) . The state equation contains a non-smooth nonlinearity, and the objective functional is convex in the control variable but contains non-smooth terms. As the mappings involved may not be Gâteaux differentiable, we use a regularization technique to regularize these nonlinear terms, aiming to obtain Gâteaux differentiable mappings. By employing this regularization technique, we are able to derive the first-order optimality condition for the regularized control problem by using the associated adjoint system. Furthermore, we conduct a limit analysis on the regularized term resulting in an optimality system for the non-smooth problem of C-stationary type. Subsequently, we establish a primal optimality condition, specifically B-stationarity. Under the assumption of “constraint qualification”, we derive the strong stationarity conditions for the non-smooth optimization problem with control constraints and establish the equivalence between B-stationarity and strong stationarity conditions.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-366034" status="VALID">
          <idno type="IdRef">028326792</idno>
          <idno type="ISNI">0000000122889830</idno>
          <idno type="ROR">https://ror.org/03rmrcq20</idno>
          <idno type="Wikidata">Q391028</idno>
          <orgName>University of British Columbia [Canada]</orgName>
          <orgName type="acronym">UBC</orgName>
          <date type="start">1908-01-01</date>
          <desc>
            <address>
              <addrLine>Vancouver Campus, 2329 West Mall, Vancouver, BC, V6T 1Z4 / Okanagan Campus, 3333 University Way, Kelowna, BC, V1V 1V7</addrLine>
              <country key="CA"/>
            </address>
            <ref type="url">https://www.ubc.ca</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-527183" status="VALID">
          <idno type="RNSR">201019055Y</idno>
          <orgName>Laboratoire de Mathématiques Informatique et Applications [UR1_1]</orgName>
          <orgName type="acronym">LAMIA</orgName>
          <desc>
            <address>
              <addrLine>Université des Antilles - Faculté des Sciences Exactes et Naturelles - Campus de Fouillole - BP 592 - 97159 Pointe-à-Pitre Cedex</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation name="UR1_1" active="#struct-524399" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-303239" status="VALID">
          <orgName>University of Puerto Rico</orgName>
          <orgName type="acronym">UPR</orgName>
          <desc>
            <address>
              <addrLine>Calle Flamboyán Jardín Botánico Sur, Río Piedras</addrLine>
              <country key="PR"/>
            </address>
            <ref type="url">http://www.upr.edu/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-524399" status="VALID">
          <idno type="IdRef">187841578</idno>
          <idno type="ROR">https://ror.org/02ryfmr77</idno>
          <orgName>Université des Antilles</orgName>
          <orgName type="acronym">UA</orgName>
          <date type="start">2015-01-01</date>
          <desc>
            <address>
              <addrLine>Université des Antilles | Fouillole - BP 250 - 97157 Pointe-à-Pitre</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-antilles.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>