<?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-03059701</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="2026-05-01T06:11:08+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Tropical Dynamic Programming for Lipschitz Multistage Stochastic Programming</title>
            <author role="aut">
              <persName>
                <forename type="first">Marianne</forename>
                <surname>Akian</surname>
              </persName>
              <idno type="halauthorid">111173-0</idno>
              <affiliation ref="#struct-450091"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Jean-Philippe</forename>
                <surname>Chancelier</surname>
              </persName>
              <email type="md5">13b64f9c9242f71340109dbf4d629714</email>
              <email type="domain">cermics.enpc.fr</email>
              <idno type="idhal" notation="string">jean-philippe-chancelier-cermics-enpc</idno>
              <idno type="idhal" notation="numeric">745318</idno>
              <idno type="halauthorid" notation="string">47837-745318</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-0658-2035</idno>
              <affiliation ref="#struct-51621"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Benoît</forename>
                <surname>Tran</surname>
              </persName>
              <email type="md5">c50975ed5e7dbd6976a9b509c91b7ae2</email>
              <email type="domain">enpc.fr</email>
              <idno type="idhal" notation="string">benoit-tran</idno>
              <idno type="idhal" notation="numeric">173454</idno>
              <idno type="halauthorid" notation="string">42874-173454</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-1344-6373</idno>
              <affiliation ref="#struct-51621"/>
              <affiliation ref="#struct-450091"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Marianne</forename>
                <surname>Akian</surname>
              </persName>
              <email type="md5">ca9847495e168bb0a4582a6d8e657df9</email>
              <email type="domain">inria.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2020-12-13 00:50:12</date>
              <date type="whenModified">2026-01-29 03:25:50</date>
              <date type="whenReleased">2020-12-13 00:50:12</date>
              <date type="whenProduced">2020-12-13</date>
              <ref type="externalLink" target="http://arxiv.org/pdf/2010.10619"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="102216">
                <persName>
                  <forename>Marianne</forename>
                  <surname>Akian</surname>
                </persName>
                <email type="md5">ca9847495e168bb0a4582a6d8e657df9</email>
                <email type="domain">inria.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03059701</idno>
            <idno type="halUri">https://inria.hal.science/hal-03059701</idno>
            <idno type="halBibtex">akian:hal-03059701</idno>
            <idno type="halRefHtml">2020</idno>
            <idno type="halRef">2020</idno>
            <availability status="restricted"/>
          </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="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INRIA">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="CERMICS" corresp="ENPC">Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique</idno>
            <idno type="stamp" n="INRIA-SACLAY" corresp="INRIA">INRIA Saclay - Ile de France</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="X-CMAP" corresp="X">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="X-DEP-MATHA">Département de mathématiques appliquées de l’École polytechnique</idno>
            <idno type="stamp" n="PARISTECH">ParisTech</idno>
            <idno type="stamp" n="INRIA_TEST">INRIA - Institut National de Recherche en Informatique et en Automatique</idno>
            <idno type="stamp" n="PREPRINT">Preprint HAL Ecole des Ponts ParisTech</idno>
            <idno type="stamp" n="TESTALAIN1">TESTALAIN1</idno>
            <idno type="stamp" n="CMAP">Centre de Mathématiques Appliquées (CMAP)</idno>
            <idno type="stamp" n="INRIA2">INRIA 2</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="GS-COMPUTER-SCIENCE">Graduate School Computer Science</idno>
            <idno type="stamp" n="DEPARTEMENT-DE-MATHEMATIQUES">Collection du Département de Mathématiques</idno>
            <idno type="stamp" n="IP-PARIS-DEPARTEMENT-MATHEMATIQUES">Département de Mathèmatiques</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">23 pages, 3 figures</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Tropical Dynamic Programming for Lipschitz Multistage Stochastic Programming</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Marianne</forename>
                    <surname>Akian</surname>
                  </persName>
                  <idno type="halauthorid">111173-0</idno>
                  <affiliation ref="#struct-450091"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Jean-Philippe</forename>
                    <surname>Chancelier</surname>
                  </persName>
                  <email type="md5">13b64f9c9242f71340109dbf4d629714</email>
                  <email type="domain">cermics.enpc.fr</email>
                  <idno type="idhal" notation="string">jean-philippe-chancelier-cermics-enpc</idno>
                  <idno type="idhal" notation="numeric">745318</idno>
                  <idno type="halauthorid" notation="string">47837-745318</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-0658-2035</idno>
                  <affiliation ref="#struct-51621"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Benoît</forename>
                    <surname>Tran</surname>
                  </persName>
                  <email type="md5">c50975ed5e7dbd6976a9b509c91b7ae2</email>
                  <email type="domain">enpc.fr</email>
                  <idno type="idhal" notation="string">benoit-tran</idno>
                  <idno type="idhal" notation="numeric">173454</idno>
                  <idno type="halauthorid" notation="string">42874-173454</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-1344-6373</idno>
                  <affiliation ref="#struct-51621"/>
                  <affiliation ref="#struct-450091"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">2010.10619</idno>
            </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="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We present an algorithm called Tropical Dynamic Programming (TDP) which builds upper and lower approximations of the Bellman value functions in risk-neutral Multistage Stochastic Programming (MSP), with independent noises of finite supports. To tackle the curse of dimensionality, popular parametric variants of Approximate Dynamic Programming approximate the Bellman value function as linear combinations of basis functions. Here, Tropical Dynamic Programming builds upper (resp. lower) approximations of a given value function as min-plus linear (resp. max-plus linear) combinations of "basic functions". At each iteration, TDP adds a new basic function to the current combination following a deterministic criterion introduced by Baucke, Downward and Zackeri in 2018 for a variant of Stochastic Dual Dynamic Programming. We prove, for every Lipschitz MSP, the asymptotic convergence of the generated approximating functions of TDP to the Bellman value functions on sets of interest. We illustrate this result on MSP with linear dynamics and polyhedral costs.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="researchteam" xml:id="struct-450091" status="VALID">
          <idno type="RNSR">201621988K</idno>
          <idno type="ROR">https://ror.org/04fvec703</idno>
          <orgName>Méthodes tropicales: structures, algorithmes et interactions</orgName>
          <orgName type="acronym">TROPICAL</orgName>
          <date type="start">2016-01-01</date>
          <date type="end">2026-12-31</date>
          <desc>
            <address>
              <addrLine>1 Rue Honoré d'Estienne d'Orves91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/equipes/tropical</ref>
          </desc>
          <listRelation>
            <relation active="#struct-89626" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
            <relation active="#struct-300340" type="indirect"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="indirect"/>
            <relation active="#struct-1225635" type="direct"/>
            <relation active="#struct-118511" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-51621" status="OLD">
          <idno type="IdRef">151174822</idno>
          <idno type="ISNI">0000000403826254</idno>
          <idno type="RNSR">200320607R</idno>
          <idno type="ROR">https://ror.org/03wct8w46</idno>
          <idno type="Wikidata">Q51781803</idno>
          <orgName>Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique</orgName>
          <orgName type="acronym">CERMICS</orgName>
          <date type="end">2024-12-31</date>
          <desc>
            <address>
              <addrLine>6 et 8 avenue Blaise Pascal Cité Descartes - Champs sur Marne 77455 Marne la Vallée Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://cermics.enpc.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301545" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-89626" status="VALID">
          <idno type="IdRef">197373461</idno>
          <idno type="ISNI">000000010944436X</idno>
          <idno type="RNSR">199719340P</idno>
          <idno type="ROR">https://ror.org/012e1xn46</idno>
          <idno type="Wikidata">Q16008922</idno>
          <orgName>Centre de Mathématiques Appliquées de l'Ecole polytechnique</orgName>
          <orgName type="acronym">CMAP</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Route de Saclay, 91128 Palaiseau Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://cmap.ip-paris.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" type="direct"/>
            <relation active="#struct-300340" type="direct"/>
            <relation active="#struct-563936" type="indirect"/>
            <relation name="UMR7641" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300009" status="VALID">
          <idno type="ROR">https://ror.org/02kvxyf05</idno>
          <orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
          <orgName type="acronym">Inria</orgName>
          <desc>
            <address>
              <addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/en/</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>
        <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="department" xml:id="struct-1225635" status="VALID">
          <idno type="ROR">https://ror.org/026839t73</idno>
          <orgName>Centre Inria de l'Institut Polytechnique de Paris</orgName>
          <date type="start">2022-11-01</date>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'Orves –Bâtiment Alan Turing –Campus de l'École Polytechnique –91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-118511" type="direct"/>
            <relation active="#struct-300009" type="indirect"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-118511" status="VALID">
          <idno type="RNSR">200818248E</idno>
          <idno type="ROR">https://ror.org/0315e5x55</idno>
          <orgName>Centre Inria de Saclay</orgName>
          <desc>
            <address>
              <addrLine>1 rue Honoré d'Estienne d'OrvesBâtiment Alan TuringCampus de l'École Polytechnique91120 Palaiseau</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.inria.fr/centre/saclay</ref>
          </desc>
          <listRelation>
            <relation active="#struct-300009" 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>
      </listOrg>
    </back>
  </text>
</TEI>