<?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-03339887v2</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="2026-05-16T19:33:05+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Convergent algorithms for a class of convex semi-infinite programs</title>
            <author role="aut">
              <persName>
                <forename type="first">Martina</forename>
                <surname>Cerulli</surname>
              </persName>
              <idno type="halauthorid">46941-0</idno>
              <affiliation ref="#struct-301020"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Antoine</forename>
                <surname>Oustry</surname>
              </persName>
              <idno type="halauthorid">42234-0</idno>
              <affiliation ref="#struct-2071"/>
              <affiliation ref="#struct-301545"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Claudia</forename>
                <surname>d'Ambrosio</surname>
              </persName>
              <email type="md5">424a46cff777aeb348e3c3633e5f53f8</email>
              <email type="domain">lix.polytechnique.fr</email>
              <idno type="idhal" notation="string">claudia-dambrosio</idno>
              <idno type="idhal" notation="numeric">735888</idno>
              <idno type="halauthorid" notation="string">46940-735888</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-4040-0960</idno>
              <affiliation ref="#struct-2071"/>
              <affiliation ref="#struct-1076966"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Leo</forename>
                <surname>Liberti</surname>
              </persName>
              <email type="md5">25d89f16c9bccad2924e186a0b563933</email>
              <email type="domain">gmail.com</email>
              <idno type="idhal" notation="string">leoliberti</idno>
              <idno type="idhal" notation="numeric">184522</idno>
              <idno type="halauthorid" notation="string">3712-184522</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-3139-6821</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.com/citations?user=6npyGgEAAAAJ</idno>
              <idno type="IDREF">https://www.idref.fr/135962404</idno>
              <affiliation ref="#struct-1076966"/>
              <affiliation ref="#struct-2071"/>
              <affiliation ref="#struct-441569"/>
              <affiliation ref="#struct-300340"/>
              <affiliation ref="#struct-563936"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Martina</forename>
                <surname>Cerulli</surname>
              </persName>
              <email type="md5">c870456f8402709ac7dc4374dfe4dc47</email>
              <email type="domain">unisa.it</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2021-09-09 17:12:03</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2022-02-22 13:19:40</date>
              <date type="whenModified">2025-10-18 03:29:20</date>
              <date type="whenReleased">2022-03-14 15:17:49</date>
              <date type="whenProduced">2022</date>
              <date type="whenEndEmbargoed">2022-02-22</date>
              <ref type="file" target="https://hal.science/hal-03339887v2/document">
                <date notBefore="2022-02-22"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-03339887v2/file/convergent-algorithms-for-SIP.pdf" id="file-3584298-3135131">
                <date notBefore="2022-02-22"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="682469">
                <persName>
                  <forename>Martina</forename>
                  <surname>Cerulli</surname>
                </persName>
                <email type="md5">c870456f8402709ac7dc4374dfe4dc47</email>
                <email type="domain">unisa.it</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03339887</idno>
            <idno type="halUri">https://hal.science/hal-03339887</idno>
            <idno type="halBibtex">cerulli:hal-03339887</idno>
            <idno type="halRefHtml">&lt;i&gt;SIAM Journal on Optimization&lt;/i&gt;, In press, 32 (4), pp.2493-2526. &lt;a target="_blank" href="https://dx.doi.org/10.1137/21M1431047"&gt;&amp;#x27E8;10.1137/21M1431047&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">SIAM Journal on Optimization, In press, 32 (4), pp.2493-2526. &amp;#x27E8;10.1137/21M1431047&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3584298-3135131"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="X">École polytechnique</idno>
            <idno type="stamp" n="ENPC" corresp="PARISTECH">École nationale des ponts et chaussées </idno>
            <idno type="stamp" n="ESSEC">ESSEC Business School</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="LIX" corresp="X">Laboratoire d'informatique de l'Ecole polytechnique</idno>
            <idno type="stamp" n="X-DEP-INFO">Département d'informatique de l’École polytechnique</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</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="IP_PARIS">Institut Polytechnique de Paris</idno>
            <idno type="stamp" n="DEPARTEMENT-DE-MATHEMATIQUES">Collection du Département de Mathématiques</idno>
            <idno type="stamp" n="IP-PARIS-INFORMATIQUE-DONNEES-ET-IA">IP Paris Département d'Informatique, de Données et d'IA</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">Convergent algorithms for a class of convex semi-infinite programs</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Martina</forename>
                    <surname>Cerulli</surname>
                  </persName>
                  <idno type="halauthorid">46941-0</idno>
                  <affiliation ref="#struct-301020"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Antoine</forename>
                    <surname>Oustry</surname>
                  </persName>
                  <idno type="halauthorid">42234-0</idno>
                  <affiliation ref="#struct-2071"/>
                  <affiliation ref="#struct-301545"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Claudia</forename>
                    <surname>d'Ambrosio</surname>
                  </persName>
                  <email type="md5">424a46cff777aeb348e3c3633e5f53f8</email>
                  <email type="domain">lix.polytechnique.fr</email>
                  <idno type="idhal" notation="string">claudia-dambrosio</idno>
                  <idno type="idhal" notation="numeric">735888</idno>
                  <idno type="halauthorid" notation="string">46940-735888</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-4040-0960</idno>
                  <affiliation ref="#struct-2071"/>
                  <affiliation ref="#struct-1076966"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Leo</forename>
                    <surname>Liberti</surname>
                  </persName>
                  <email type="md5">25d89f16c9bccad2924e186a0b563933</email>
                  <email type="domain">gmail.com</email>
                  <idno type="idhal" notation="string">leoliberti</idno>
                  <idno type="idhal" notation="numeric">184522</idno>
                  <idno type="halauthorid" notation="string">3712-184522</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-3139-6821</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.com/citations?user=6npyGgEAAAAJ</idno>
                  <idno type="IDREF">https://www.idref.fr/135962404</idno>
                  <affiliation ref="#struct-1076966"/>
                  <affiliation ref="#struct-2071"/>
                  <affiliation ref="#struct-441569"/>
                  <affiliation ref="#struct-300340"/>
                  <affiliation ref="#struct-563936"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">8480</idno>
                <idno type="issn">1052-6234</idno>
                <title level="j">SIAM Journal on Optimization</title>
                <imprint>
                  <publisher>Society for Industrial and Applied Mathematics</publisher>
                  <biblScope unit="volume">32</biblScope>
                  <biblScope unit="issue">4</biblScope>
                  <biblScope unit="pp">2493-2526</biblScope>
                  <date type="datePub" subtype="inPress">2022</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1137/21M1431047</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Cutting Plane</term>
                <term xml:lang="en">Semidefinite programming</term>
                <term xml:lang="en">Semi-infinite programming</term>
              </keywords>
              <classCode scheme="halDomain" n="math.math-oc">Mathematics [math]/Optimization and Control [math.OC]</classCode>
              <classCode scheme="halDomain" n="info.info-ro">Computer Science [cs]/Operations Research [math.OC]</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>We focus on convex semi-infinite programs with an infinite number of quadratically parametrized constraints. In our setting, the lower-level problem, i.e., the problem of finding the constraint that is the most violated by a given point, is not necessarily convex. We propose a new convergent approach to solve these semi-infinite programs. Based on the Lagrangian dual of the lower-level problem, we derive a convex and tractable restriction of the considered semi-infinite programming problem. We state sufficient conditions for the optimality of this restriction. If these conditions are not met, the restriction is enlarged through an Inner-Outer Approximation Algorithm, and its value converges to the value of the original semi-infinite problem. This new algorithmic approach is compared with the classical Cutting Plane algorithm. We also propose a new rate of convergence of the Cutting Plane algorithm, directly related to the iteration index, derived when the objective function is strongly convex, and under a strict feasibility assumption. We successfully test the two methods on two applications: the constrained quadratic regression and a zero-sum game with cubic payoff. Our results are compared to those obtained using the approach proposed in "Global optimization of semi-infinite programs via restriction of the right-hand side" by A. Mitsos (Optimization 60, 2011) as well as using the classical relaxation approach based on the KKT conditions of the lower-level problem.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="institution" xml:id="struct-301020" status="VALID">
          <idno type="IdRef">028029429</idno>
          <idno type="ROR">https://ror.org/02dga6j42</idno>
          <orgName>ESSEC Business School</orgName>
          <desc>
            <address>
              <addrLine>1, avenue Bernard HirschCS 50105 Cergy95021 Cergy Pontoise CedexFranceTél : +33 (0)1 34 43 30 00Fax : +33 (0)1 34 43 30 01</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.essec.edu</ref>
          </desc>
        </org>
        <org type="laboratory" xml:id="struct-2071" status="VALID">
          <idno type="IdRef">196509955</idno>
          <idno type="ISNI">0000000403673665</idno>
          <idno type="RNSR">200519331V</idno>
          <idno type="ROR">https://ror.org/04afed728</idno>
          <idno type="Wikidata">Q16009025</idno>
          <orgName>Laboratoire d'informatique de l'École polytechnique [Palaiseau]</orgName>
          <orgName type="acronym">LIX</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>1 Rue Honoré d’Estienne d’Orves, Bâtiment Alain Turing, 91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.lix.polytechnique.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7161" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-301545" status="OLD">
          <idno type="ROR">https://ror.org/02nwvxz07</idno>
          <orgName>École nationale des ponts et chaussées</orgName>
          <orgName type="acronym">ENPC</orgName>
          <date type="start">1747-02-14</date>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>École nationale des ponts et chaussées, 6-8 avenue Blaise-Pascal, Cité Descartes, Champs-sur-Marne, 77455 Marne-la-Vallée cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://ecoledesponts.fr/</ref>
          </desc>
        </org>
        <org type="researchteam" xml:id="struct-1076966" status="VALID">
          <orgName>Optimization at LIX</orgName>
          <orgName type="acronym">OptimiX</orgName>
          <date type="start">2021-01-21</date>
          <desc>
            <address>
              <addrLine>LIX CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://optimix.cnrs.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-2071" type="direct"/>
            <relation active="#struct-300340" type="indirect"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7161" active="#struct-441569" type="indirect"/>
          </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-300340" status="VALID">
          <idno type="IdRef">027309320</idno>
          <idno type="ISNI">0000000121581279</idno>
          <idno type="ROR">https://ror.org/05hy3tk52</idno>
          <idno type="Wikidata">Q273626</idno>
          <orgName>École polytechnique</orgName>
          <orgName type="acronym">X</orgName>
          <date type="start">1794-03-11</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.polytechnique.edu/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-563936" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-563936" status="VALID">
          <idno type="IdRef">238327159</idno>
          <idno type="ISNI">0000000502717600</idno>
          <idno type="ROR">https://ror.org/042tfbd02</idno>
          <idno type="Wikidata">Q48759778</idno>
          <orgName>Institut Polytechnique de Paris</orgName>
          <orgName type="acronym">IP Paris</orgName>
          <date type="start">2019-06-02</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91120 Palaiseau Cedex, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.ip-paris.fr</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>