{"id":"https://openalex.org/W7214939014","doi":"https://doi.org/10.48550/arxiv.2609.37286","title":"Extension on the convergence rates of moment-SOS hierarchies via approximation of truncated moment sequences","display_name":"Extension on the convergence rates of moment-SOS hierarchies via approximation of truncated moment sequences","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214939014","doi":"https://doi.org/10.48550/arxiv.2609.37286"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37286","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37286","pdf_url":"https://arxiv.org/pdf/2609.37286","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.37286","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086561487","display_name":"Hoang Tran","orcid":"https://orcid.org/0000-0001-7068-5621","observed_orcids":["https://orcid.org/0000-0001-7068-5621"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tran, Hoang Anh","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5064083862","display_name":"Kim-Chuan Toh","orcid":"https://orcid.org/0000-0001-7204-8933","observed_orcids":["https://orcid.org/0000-0001-7204-8933"]},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I4405277661","display_name":"Institute of Operations Research and Analytics","ror":"https://ror.org/03gr3d554","country_code":"SG","type":"facility","lineage":["https://openalex.org/I4405277661"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Toh, Kim-Chuan","raw_affiliation_strings":["Department of Mathematics , and Institute of Operations Research and Analytics , National University of Singapore , Singapore 119076"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , and Institute of Operations Research and Analytics , National University of Singapore , Singapore 119076","institution_ids":["https://openalex.org/I165932596","https://openalex.org/I4405277661"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9961000084877014,"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":0.9961000084877014,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.0003000000142492354,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/moment-sos-hierarchy","display_name":"moment-SOS hierarchy","score":0.8980000019073486},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.9570000171661377},{"id":"https://openalex.org/keywords/ojasiewicz-inequality","display_name":"\u0141ojasiewicz inequality","score":0.8579999804496765},{"id":"https://openalex.org/keywords/representing-measures","display_name":"representing measures","score":0.7680000066757202}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7657999992370605},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.7364000082015991},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6060000061988831},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.5735999941825867},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5705000162124634},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5663999915122986},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5504000186920166},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5163999795913696},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4787999987602234},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4708000123500824},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.414000004529953},{"id":"https://openalex.org/C4285052","wikidata":"https://www.wikidata.org/wiki/Q3406268","display_name":"Moment problem","level":3,"score":0.4027000069618225},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.36570000648498535},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3061000108718872},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.3052000105381012},{"id":"https://openalex.org/C157709441","wikidata":"https://www.wikidata.org/wiki/Q1411887","display_name":"Uniform convergence","level":3,"score":0.3012000024318695},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2969000041484833},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.26429998874664307},{"id":"https://openalex.org/C95763700","wikidata":"https://www.wikidata.org/wiki/Q578985","display_name":"Convergence of random variables","level":3,"score":0.25540000200271606},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37286","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37286","pdf_url":"https://arxiv.org/pdf/2609.37286","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.37286","doi":"https://doi.org/10.48550/arxiv.2609.37286","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37286","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.37286","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37286","pdf_url":"https://arxiv.org/pdf/2609.37286","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214939014.pdf","grobid_xml":"https://content.openalex.org/works/W7214939014.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4414746157","https://openalex.org/W6966865005","https://openalex.org/W7161545632","https://openalex.org/W7163031925","https://openalex.org/W7213581190"],"related_works":["https://openalex.org/W4416886382","https://openalex.org/W4391421601","https://openalex.org/W4416615175","https://openalex.org/W3105363210","https://openalex.org/W7213581190","https://openalex.org/W4225852106","https://openalex.org/W3003854559","https://openalex.org/W4376116059","https://openalex.org/W4392636743","https://openalex.org/W4287330157"],"abstract_inverted_index":{"This":[0],"paper":[1],"continues":[2],"our":[3],"work":[4],"on":[5],"the":[6,20,24,28,56,63,72,75,82,85],"convergence":[7],"rates":[8],"of":[9,14,58],"moment-SOS":[10],"hierarchies":[11],"via":[12],"approximation":[13],"truncated":[15],"moment":[16,52],"sequences.":[17],"We":[18],"extend":[19],"method":[21],"developed":[22],"for":[23],"Schm\u00fcdgen-type":[25],"hierarchy":[26],"to":[27,39,44],"Putinar-type,":[29],"Krivine--Stengle-type,":[30],"extended-Handelman-type,":[31],"and":[32,54],"Hol-Scherer-type":[33],"hierarchies.":[34],"The":[35,67],"main":[36],"idea":[37],"is":[38],"lift":[40],"a":[41,45,51,59],"pseudo-moment":[42],"sequence":[43],"simple":[46],"set,":[47],"approximate":[48],"it":[49],"by":[50],"sequence,":[53],"project":[55],"atoms":[57],"representing":[60],"measure":[61],"onto":[62],"original":[64],"feasible":[65],"set.":[66],"\u0141ojasiewicz":[68,86],"inequality":[69],"then":[70],"converts":[71],"error":[73,80],"in":[74,81],"defining":[76],"constraints":[77],"into":[78],"an":[79],"moments.":[83],"With":[84],"exponent":[87],"$0":[88]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}