{"id":"https://openalex.org/W4386623328","doi":"https://doi.org/10.1017/s0962492923000053","title":"The Moment-SOS hierarchy: Applications and related topics","display_name":"The Moment-SOS hierarchy: Applications and related topics","publication_year":2024,"publication_date":"2024-07-01","ids":{"openalex":"https://openalex.org/W4386623328","doi":"https://doi.org/10.1017/s0962492923000053"},"language":"en","primary_location":{"id":"doi:10.1017/s0962492923000053","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0962492923000053","pdf_url":null,"source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://laas.hal.science/hal-04201167v1/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006670993","display_name":"Jean B. Lasserre","orcid":"https://orcid.org/0000-0003-0860-9913"},"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/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I190497903","https://openalex.org/I193033237","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210152422","https://openalex.org/I4210159245","https://openalex.org/I4405258862","https://openalex.org/I4405259414"]},{"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/I1294671590","https://openalex.org/I4210092408"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean B. Lasserre","raw_affiliation_strings":["LAAS-CNRS and Toulouse School of Economics (TSE), University of Toulouse, 7 Avenue du Colonel Roche, BP54200, 31031 Toulouse c\u00e9dex 4, France E-mail:","LAAS-POP - Equipe Polynomial OPtimization (France)"],"raw_orcid":"https://orcid.org/0000-0003-0860-9913","affiliations":[{"raw_affiliation_string":"LAAS-CNRS and Toulouse School of Economics (TSE), University of Toulouse, 7 Avenue du Colonel Roche, BP54200, 31031 Toulouse c\u00e9dex 4, France E-mail:","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I17866349","https://openalex.org/I190497903","https://openalex.org/I4210092408"]},{"raw_affiliation_string":"LAAS-POP - Equipe Polynomial OPtimization (France)","institution_ids":["https://openalex.org/I190497903"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5006670993"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I17866349","https://openalex.org/I190497903","https://openalex.org/I4210092408"],"apc_list":null,"apc_paid":null,"fwci":2.73,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.8863526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"33","issue":null,"first_page":"841","last_page":"908"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.21899999678134918,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.21899999678134918,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.2045000046491623,"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"}},{"id":"https://openalex.org/T11262","display_name":"Quantum Mechanics and Non-Hermitian Physics","score":0.07580000162124634,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.7256580591201782},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6388015747070312},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.39344215393066406},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.32272666692733765},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.18275904655456543},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15952545404434204},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.04131251573562622},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0398983359336853}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.7256580591201782},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6388015747070312},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.39344215393066406},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.32272666692733765},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.18275904655456543},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15952545404434204},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.04131251573562622},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0398983359336853}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0962492923000053","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0962492923000053","pdf_url":null,"source":{"id":"https://openalex.org/S124973578","display_name":"Acta Numerica","issn_l":"0962-4929","issn":["0962-4929","1474-0508"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Acta Numerica","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04201167v1","is_oa":true,"landing_page_url":"https://laas.hal.science/hal-04201167","pdf_url":"https://laas.hal.science/hal-04201167v1/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":"2023","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-04687963v1","is_oa":true,"landing_page_url":"https://laas.hal.science/hal-04687963","pdf_url":"https://laas.hal.science/hal-04687963v1/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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.cambridge.org/core/journals/acta-numerica","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04201167v1","is_oa":true,"landing_page_url":"https://laas.hal.science/hal-04201167","pdf_url":"https://laas.hal.science/hal-04201167v1/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":"2023","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1938070154","display_name":"Artificial and Natural Intelligence Toulouse Institute","funder_award_id":"ANR-19-P3IA-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3010527862","display_name":null,"funder_award_id":"ANR\u201019","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3879958799","display_name":null,"funder_award_id":"19-PI3A-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G602161992","display_name":null,"funder_award_id":"ANR-19-PI3A-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386623328.pdf","grobid_xml":"https://content.openalex.org/works/W4386623328.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2365264209","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W962203960","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2026999166"],"abstract_inverted_index":{"The":[0],"Moment-SOS":[1,118],"hierarchy,":[2],"first":[3],"introduced":[4],"in":[5,7,81,95,99],"optimization":[6,96],"2000,":[8],"is":[9,88],"based":[10],"on":[11,27,59],"the":[12,15,71,109,117],"theory":[13],"of":[14,70,78,84],"S":[16,28],"-moment":[17],"problem":[18,74],"and":[19,86,97,112,120],"its":[20,114],"dual":[21],"counterpart:":[22],"polynomials":[23],"that":[24,33],"are":[25],"positive":[26,121],".":[29],"It":[30],"turns":[31],"out":[32],"this":[34,93],"methodology":[35,94],"can":[36,64],"also":[37,98,107],"be":[38,65],"used":[39],"to":[40],"solve":[41],"problems":[42,63],"with":[43,116],"positivity":[44],"constraints":[45,58],"\u2018":[46],"f":[47],"(x)":[48],"\u2265":[49],"0":[50],"for":[51,103],"all":[52],"$\\mathbf{x}\\in":[53],"S$":[54],"\u2019":[55],"or":[56],"linear":[57],"Borel":[60],"measures.":[61],"Such":[62],"viewed":[66],"as":[67],"specific":[68],"instances":[69],"generalized":[72],"moment":[73],"(GMP),":[75],"whose":[76],"list":[77],"important":[79],"applications":[80,102],"various":[82],"domains":[83],"science":[85],"engineering":[87],"almost":[89],"endless.":[90],"We":[91],"describe":[92],"two":[100],"other":[101],"illustration.":[104],"Finally":[105],"we":[106],"introduce":[108],"Christoffel":[110],"function":[111],"reveal":[113],"links":[115],"hierarchy":[119],"polynomials.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}