{"id":"https://openalex.org/W4399151428","doi":"https://doi.org/10.1287/moor.2024.0550","title":"On the Sequential Convergence of Lloyd\u2019s Algorithms","display_name":"On the Sequential Convergence of Lloyd\u2019s Algorithms","publication_year":2025,"publication_date":"2025-05-09","ids":{"openalex":"https://openalex.org/W4399151428","doi":"https://doi.org/10.1287/moor.2024.0550"},"language":"en","primary_location":{"id":"doi:10.1287/moor.2024.0550","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2024.0550","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2405.20744","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102678883","display_name":"L\u00e9o Portales","orcid":null},"institutions":[{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I205747304","display_name":"Institut National Polytechnique de Toulouse","ror":"https://ror.org/033p9g875","country_code":"FR","type":"education","lineage":["https://openalex.org/I205747304"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210092408","display_name":"Toulouse School of Economics","ror":"https://ror.org/00ff5f522","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210092408"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Leo Portales","raw_affiliation_strings":["Toulouse Research Institute in Information Technology, Toulouse School of Economics, National Polytechnic Institute of Toulouse, University of Toulouse, 31000 Toulouse, France","Toulouse INP - Institut National Polytechnique (Toulouse) (France)","TSE-R - Toulouse School of Economics (Manufacture de Tabacs, 21 all\u00e9es de Brienne 31000 Toulouse - France)","IRIT-SC - Signal et Communications (IRIT\r\n2 rue Charles Camichel \r\n31071 Toulouse Cedex 7 - France)"],"raw_orcid":"https://orcid.org/0009-0007-3075-227X","affiliations":[{"raw_affiliation_string":"Toulouse Research Institute in Information Technology, Toulouse School of Economics, National Polytechnic Institute of Toulouse, University of Toulouse, 31000 Toulouse, France","institution_ids":["https://openalex.org/I205747304","https://openalex.org/I4210092408"]},{"raw_affiliation_string":"Toulouse INP - Institut National Polytechnique (Toulouse) (France)","institution_ids":["https://openalex.org/I205747304"]},{"raw_affiliation_string":"TSE-R - Toulouse School of Economics (Manufacture de Tabacs, 21 all\u00e9es de Brienne 31000 Toulouse - France)","institution_ids":["https://openalex.org/I4210092408"]},{"raw_affiliation_string":"IRIT-SC - Signal et Communications (IRIT\r\n2 rue Charles Camichel \r\n31071 Toulouse Cedex 7 - France)","institution_ids":["https://openalex.org/I4210152422","https://openalex.org/I134560555","https://openalex.org/I4210119061","https://openalex.org/I3131550300","https://openalex.org/I4210160189"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028493116","display_name":"Elsa Cazelles","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I134560555","display_name":"Universit\u00e9 Toulouse III - Paul Sabatier","ror":"https://ror.org/02v6kpv12","country_code":"FR","type":"education","lineage":["https://openalex.org/I134560555"]},{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210119061","display_name":"Institut de Recherche en Informatique de Toulouse","ror":"https://ror.org/01rx4qw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210119061","https://openalex.org/I4210152422","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"id":"https://openalex.org/I4210152422","display_name":"Universit\u00e9 Toulouse - Jean Jaur\u00e8s","ror":"https://ror.org/04ezk3x31","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210152422"]},{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Elsa Cazelles","raw_affiliation_strings":["CNRS, Toulouse Research Institute in Information Technology, University of Toulouse, 31000 Toulouse, France","CNRS - Centre National de la Recherche Scientifique (France)","IRIT-SC - Signal et Communications (IRIT\r\n2 rue Charles Camichel \r\n31071 Toulouse Cedex 7 - France)"],"raw_orcid":"https://orcid.org/0000-0002-7444-0274","affiliations":[{"raw_affiliation_string":"CNRS, Toulouse Research Institute in Information Technology, University of Toulouse, 31000 Toulouse, France","institution_ids":["https://openalex.org/I4210119061","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS - Centre National de la Recherche Scientifique (France)","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"IRIT-SC - Signal et Communications (IRIT\r\n2 rue Charles Camichel \r\n31071 Toulouse Cedex 7 - France)","institution_ids":["https://openalex.org/I4210152422","https://openalex.org/I134560555","https://openalex.org/I4210119061","https://openalex.org/I3131550300","https://openalex.org/I4210160189"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067908150","display_name":"Edouard Pauwels","orcid":"https://orcid.org/0000-0002-8180-075X"},"institutions":[{"id":"https://openalex.org/I3131550300","display_name":"Universit\u00e9 Toulouse-I-Capitole","ror":"https://ror.org/0443n9e75","country_code":"FR","type":"education","lineage":["https://openalex.org/I3131550300"]},{"id":"https://openalex.org/I4210092408","display_name":"Toulouse School of Economics","ror":"https://ror.org/00ff5f522","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210092408"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Edouard Pauwels","raw_affiliation_strings":["Toulouse School of Economics, University of Toulouse Capitole, 31080 Toulouse, France","TSE-R - Toulouse School of Economics (Manufacture de Tabacs, 21 all\u00e9es de Brienne 31000 Toulouse - France)","UT Capitole - Universit\u00e9 Toulouse Capitole (2 rue du Doyen-Gabriel-Marty - 31042 Toulouse Cedex 9 - France)"],"raw_orcid":"https://orcid.org/0000-0002-8180-075X","affiliations":[{"raw_affiliation_string":"Toulouse School of Economics, University of Toulouse Capitole, 31080 Toulouse, France","institution_ids":["https://openalex.org/I4210092408"]},{"raw_affiliation_string":"TSE-R - Toulouse School of Economics (Manufacture de Tabacs, 21 all\u00e9es de Brienne 31000 Toulouse - France)","institution_ids":["https://openalex.org/I4210092408"]},{"raw_affiliation_string":"UT Capitole - Universit\u00e9 Toulouse Capitole (2 rue du Doyen-Gabriel-Marty - 31042 Toulouse Cedex 9 - France)","institution_ids":["https://openalex.org/I3131550300"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":8,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9122,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.72669015,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"51","issue":"2","first_page":"1120","last_page":"1138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9873999953269958,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.9753000140190125,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5607852339744568},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5458900332450867},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5300031900405884},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.07533732056617737}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5607852339744568},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5458900332450867},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5300031900405884},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.07533732056617737},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1287/moor.2024.0550","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2024.0550","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:publications.ut-capitole.fr:51796","is_oa":false,"landing_page_url":"https://www.idref.fr/297472518>","pdf_url":null,"source":{"id":"https://openalex.org/S4306401603","display_name":"Toulouse Capitole Publications (University Toulouse 1 Capitole)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I3131550300","host_organization_name":"Universit\u00e9 Toulouse-I-Capitole","host_organization_lineage":["https://openalex.org/I3131550300"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:arXiv.org:2405.20744","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2405.20744","pdf_url":"https://arxiv.org/pdf/2405.20744","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-04593982v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04593982","pdf_url":"https://hal.science/hal-04593982/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.science/hal-04593982","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2405.20744","is_oa":true,"landing_page_url":"https://arxiv.org/abs/2405.20744","pdf_url":"https://arxiv.org/pdf/2405.20744","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1141025942","display_name":"Toulouse Graduate School d\u00e9fis en \u00e9conomie et sciences sociales quantitatives","funder_award_id":"ANR-17-EURE-0010","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2267958192","display_name":null,"funder_award_id":"17-EURE-0010","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G2659019386","display_name":null,"funder_award_id":"ANR-17-EURE-","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3257071504","display_name":null,"funder_award_id":"FA8655-22-1-7012","funder_id":"https://openalex.org/F4320332467","funder_display_name":"U.S. Air Force"},{"id":"https://openalex.org/G4706302943","display_name":"Mathematics of Automatic Differentiation","funder_award_id":"ANR-24-CE23-1529","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5777575804","display_name":null,"funder_award_id":"ANR-19-PI3A0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6612625481","display_name":null,"funder_award_id":"France 2030","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6803667113","display_name":null,"funder_award_id":"ANR-17","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7506056258","display_name":"Numerical analysis, optimal control and optimal transport for AI","funder_award_id":"ANR-23-PEIA-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8318455765","display_name":null,"funder_award_id":"ANR-19","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322893","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"},{"id":"https://openalex.org/F4320338463","display_name":"CHIST-ERA","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4399151428.pdf","grobid_xml":"https://content.openalex.org/works/W4399151428.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W26023427","https://openalex.org/W179029813","https://openalex.org/W182620070","https://openalex.org/W385466589","https://openalex.org/W1576475658","https://openalex.org/W1585160083","https://openalex.org/W1588048250","https://openalex.org/W1873407551","https://openalex.org/W1967138577","https://openalex.org/W1981369974","https://openalex.org/W1984609374","https://openalex.org/W2006444496","https://openalex.org/W2009803967","https://openalex.org/W2014185065","https://openalex.org/W2019106840","https://openalex.org/W2019534414","https://openalex.org/W2021361347","https://openalex.org/W2022541060","https://openalex.org/W2027982384","https://openalex.org/W2033497516","https://openalex.org/W2042436556","https://openalex.org/W2046046781","https://openalex.org/W2048531373","https://openalex.org/W2049153601","https://openalex.org/W2051752778","https://openalex.org/W2065978712","https://openalex.org/W2077612096","https://openalex.org/W2078853581","https://openalex.org/W2087566144","https://openalex.org/W2107649935","https://openalex.org/W2117411139","https://openalex.org/W2129732816","https://openalex.org/W2150593711","https://openalex.org/W2157673273","https://openalex.org/W2171056260","https://openalex.org/W2185948302","https://openalex.org/W2266445751","https://openalex.org/W2346626577","https://openalex.org/W2559655401","https://openalex.org/W2766276860","https://openalex.org/W2913142797","https://openalex.org/W2962826994","https://openalex.org/W2962870332","https://openalex.org/W2963160215","https://openalex.org/W2990138404","https://openalex.org/W3082525919","https://openalex.org/W4206471589","https://openalex.org/W4250171872","https://openalex.org/W4253577938","https://openalex.org/W4255839052","https://openalex.org/W4281661032","https://openalex.org/W4288607991","https://openalex.org/W4379231033"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"Lloyd\u2019s":[0,65,130],"algorithm":[1,32],"is":[2,25,46],"an":[3,71,95],"iterative":[4],"method":[5,39,131],"that":[6,11],"solves":[7],"the":[8,13,53,92,99,102,120,127,137,168,173,187,192,198,203,209,221,226],"quantization":[9,43,69,78],"problem,":[10],"is,":[12],"approximation":[14],"of":[15,64,91,101,123,129,140,230],"a":[16,21,37,41,57,80,113,133,147],"target":[17,103],"probability":[18],"measure":[19,74],"by":[20,48,191],"discrete":[22,73,82],"one,":[23],"and":[24,75,136,172,212,244,254],"particularly":[26],"used":[27],"in":[28],"digital":[29],"applications.":[30],"This":[31,105,180],"can":[33],"be":[34],"interpreted":[35],"as":[36,132,162],"gradient":[38,134,141],"on":[40,98],"certain":[42],"functional":[44],"which":[45],"given":[47],"optimal":[49,68,158,176],"transport.":[50],"We":[51],"study":[52],"sequential":[54,89],"convergence":[55,90,138],"(to":[56],"single":[58],"accumulation":[59],"point)":[60],"for":[61,107,154,195,220],"two":[62],"variants":[63],"method:":[66],"(i)":[67],"with":[70,79,165,202],"arbitrary":[72],"(ii)":[76],"uniform":[77,81],"measure.":[83,104],"For":[84],"both":[85],"cases,":[86],"we":[87,149],"prove":[88],"iterates":[93],"under":[94,143,197],"analyticity":[96],"assumption":[97],"density":[100],"includes":[106],"example":[108],"analytic":[109],"densities":[110],"truncated":[111],"to":[112],"compact":[114],"semialgebraic":[115],"set.":[116],"The":[117],"argument":[118],"leverages":[119],"log-analytic":[121],"nature":[122],"globally":[124],"subanalytic":[125],"integrals,":[126],"interpretation":[128],"method,":[135],"analysis":[139],"algorithms":[142],"Kurdyka\u2013\u0141ojasiewicz":[144],"assumptions.":[145],"As":[146],"by-product,":[148],"also":[150],"obtain":[151],"definability":[152],"results":[153],"more":[155],"general":[156,166],"semidiscrete":[157],"transport":[159,163,177],"losses":[160],"such":[161],"distances":[164],"costs,":[167],"max-sliced":[169],"Wasserstein":[170],"distance,":[171],"entropy":[174],"regularized":[175],"loss.":[178],"Funding:":[179],"work":[181],"benefited":[182],"from":[183,186,247],"financial":[184],"support":[185,246],"French":[188,218],"government":[189],"managed":[190],"National":[193],"Agency":[194],"Research":[196],"France":[199],"2030":[200],"program,":[201],"reference":[204],"\u201cANR-23-PEIA-0004\u201d.":[205],"E.":[206],"Pauwels":[207],"thanks":[208],"3IA":[210],"Artificial":[211],"Natural":[213],"Intelligence":[214],"Toulouse":[215],"Institute":[216],"(ANITI),":[217],"\u201cInvesting":[219],"Future\u2014PIA3\u201d":[222],"program":[223],"[Grant":[224,237,250,257],"ANR-19-PI3A-000],":[225],"Air":[227,233],"Force":[228,234],"Office":[229],"Scientific":[231],"Research,":[232],"Material":[235],"Command":[236],"FA8655-22-1-7012],":[238],"TSE-P,":[239],"Institut":[240],"Universitaire":[241],"de":[242],"France,":[243],"acknowledges":[245],"ANR":[248,252,255],"Chess":[249],"ANR-17-EURE-0010],":[251],"Regulia":[253],"MAD":[256],"ANR-24-CE23-1529-02].":[258]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-04T07:58:01.006859","created_date":"2025-10-10T00:00:00"}
