{"id":"https://openalex.org/W3135880998","doi":"https://doi.org/10.1007/s11590-022-01851-3","title":"Convergence rates of RLT and Lasserre-type hierarchies for the generalized moment problem over the simplex and the sphere","display_name":"Convergence rates of RLT and Lasserre-type hierarchies for the generalized moment problem over the simplex and the sphere","publication_year":2022,"publication_date":"2022-02-01","ids":{"openalex":"https://openalex.org/W3135880998","doi":"https://doi.org/10.1007/s11590-022-01851-3","mag":"3135880998"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-022-01851-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-022-01851-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-022-01851-3.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11590-022-01851-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5042455940","display_name":"Felix Kirschner","orcid":"https://orcid.org/0000-0003-1771-0394"},"institutions":[{"id":"https://openalex.org/I193700539","display_name":"Tilburg University","ror":"https://ror.org/04b8v1s79","country_code":"NL","type":"education","lineage":["https://openalex.org/I193700539"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Felix Kirschner","raw_affiliation_strings":["Tilburg University, PO Box 90153, 5000 LE, Tilburg, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tilburg University, PO Box 90153, 5000 LE, Tilburg, The Netherlands","institution_ids":["https://openalex.org/I193700539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019341464","display_name":"Etienne de Klerk","orcid":"https://orcid.org/0000-0003-3377-0063"},"institutions":[{"id":"https://openalex.org/I193700539","display_name":"Tilburg University","ror":"https://ror.org/04b8v1s79","country_code":"NL","type":"education","lineage":["https://openalex.org/I193700539"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Etienne de Klerk","raw_affiliation_strings":["Tilburg University, PO Box 90153, 5000 LE, Tilburg, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tilburg University, PO Box 90153, 5000 LE, Tilburg, The Netherlands","institution_ids":["https://openalex.org/I193700539"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042455940"],"corresponding_institution_ids":["https://openalex.org/I193700539"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.9608,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.67123959,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"8","first_page":"2191","last_page":"2208"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9975000023841858,"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":0.9975000023841858,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9703999757766724,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.965399980545044,"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/type","display_name":"Type (biology)","score":0.6568437814712524},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.6164407730102539},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5471680164337158},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5428634881973267},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4952336847782135},{"id":"https://openalex.org/keywords/smiley","display_name":"Smiley","score":0.41480231285095215},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3538888394832611},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22778591513633728}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6568437814712524},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6164407730102539},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5471680164337158},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5428634881973267},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4952336847782135},{"id":"https://openalex.org/C2781455918","wikidata":"https://www.wikidata.org/wiki/Q11241","display_name":"Smiley","level":2,"score":0.41480231285095215},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3538888394832611},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22778591513633728},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s11590-022-01851-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-022-01851-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-022-01851-3.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},{"id":"pmh:oai:tilburguniversity.edu:openaire/3c225e7f-ae4a-4c75-8921-4babdb1af93b","is_oa":true,"landing_page_url":"https://research.tilburguniversity.edu/en/publications/3c225e7f-ae4a-4c75-8921-4babdb1af93b","pdf_url":null,"source":{"id":"https://openalex.org/S4406923027","display_name":"Tilburg University Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Kirschner, F & de Klerk, E 2022, 'Convergence rates of RLT and Lasserre-type hierarchies for the generalized moment problem over the simplex and the sphere', Optimization Letters, vol. 16, no. 8, pp. 2191\u20132208. https://doi.org/10.1007/s11590-022-01851-3","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2103.02924","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.02924","pdf_url":"https://arxiv.org/pdf/2103.02924","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-03170812v1","is_oa":true,"landing_page_url":"https://hal.science/hal-03170812","pdf_url":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2021","raw_type":"Preprints, Working Papers, ..."},{"id":"pmh:oai:RePEc:tiu:tiutis:3c225e7f-ae4a-4c75-8921-4babdb1af93b","is_oa":false,"landing_page_url":"https://repository.tilburguniversity.edu/bitstreams/6643b59b-e3b7-461a-bbfe-96aca30880a3/download","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"preprint"},{"id":"doi:10.48550/arxiv.2103.02924","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2103.02924","pdf_url":null,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s11590-022-01851-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11590-022-01851-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11590-022-01851-3.pdf","source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7001502250","display_name":"Polynomial Optimization, Efficiency through Moments and Algebra","funder_award_id":"813211","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G7534893990","display_name":"Polynomial Optimization, Efficiency through Moments and Algebra","funder_award_id":"813211","funder_id":"https://openalex.org/F4320338337","funder_display_name":"H2020 Marie Sk\u0142odowska-Curie Actions"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320338337","display_name":"H2020 Marie Sk\u0142odowska-Curie Actions","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3135880998.pdf","grobid_xml":"https://content.openalex.org/works/W3135880998.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W567568486","https://openalex.org/W1518832340","https://openalex.org/W1518992076","https://openalex.org/W1553283060","https://openalex.org/W1559197676","https://openalex.org/W1591868040","https://openalex.org/W1884347414","https://openalex.org/W1992843019","https://openalex.org/W2016403269","https://openalex.org/W2027470314","https://openalex.org/W2047577886","https://openalex.org/W2083449425","https://openalex.org/W2095886698","https://openalex.org/W2114650657","https://openalex.org/W2130010995","https://openalex.org/W2153451837","https://openalex.org/W2325692311","https://openalex.org/W2915019512","https://openalex.org/W2968911711","https://openalex.org/W2972919843","https://openalex.org/W3038798607","https://openalex.org/W6600292833"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4393105969","https://openalex.org/W4206604435","https://openalex.org/W4230651512","https://openalex.org/W2543497326","https://openalex.org/W2079103606","https://openalex.org/W3020636691","https://openalex.org/W4239597374","https://openalex.org/W2097150718","https://openalex.org/W1557860762"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"consider":[2],"the":[3,9,12,36,45,57,70,73,94,97,124,128,139,165,182],"generalized":[4],"moment":[5],"problem":[6,46],"(GMP)":[7],"over":[8,72,138,181],"simplex":[10,74],"and":[11,19,32,40,49,115],"sphere.":[13],"This":[14],"is":[15,93,169],"a":[16,60,77,86,100,110,142,170,173],"rich":[17],"setting":[18],"it":[20],"contains":[21],"NP-hard":[22],"problems":[23],"as":[24,64,66],"special":[25],"cases,":[26],"like":[27],"constructing":[28],"optimal":[29,62],"cubature":[30],"schemes":[31],"rational":[33],"optimization.":[34],"Using":[35],"reformulation-linearization":[37],"technique":[38],"(RLT)":[39],"Lasserre-type":[41],"hierarchies,":[42],"relaxations":[43],"of":[44,59,80,96,103,109,127,145,172,178],"are":[47],"introduced":[48,166,184],"analyzed.":[50],"For":[51,69],"our":[52],"analysis":[53],"we":[54,75,122,163],"assume":[55],"throughout":[56],"existence":[58],"dual":[61],"solution":[63],"well":[65],"strong":[67],"duality.":[68],"GMP":[71,129],"prove":[76,123],"convergence":[78,143],"rate":[79,144],"O":[81],"(1/":[82],"r":[83,92],")":[84,121,137],"for":[85,175],"linear":[87,167],"programming,":[88],"RLT-type":[89],"hierarchy,":[90,98],"where":[91],"level":[95],"using":[99],"quantitative":[101],"version":[102],"P\u00f3lya\u2019s":[104],"Positivstellensatz.":[105],"As":[106],"an":[107],"extension":[108],"recent":[111],"result":[112],"by":[113,185],"Fang":[114],"Fawzi":[116],"(Math":[117],"Program,":[118],"2020.":[119],"https://doi.org/10.1007/s10107-020-01537-7":[120],"Lasserre":[125],"hierarchy":[126,174],"(Lasserre":[130],"in":[131],"Math":[132],"Program":[133],"112(1):65\u201392,":[134],"2008.":[135],"https://doi.org/10.1007/s10107-006-0085-1":[136],"sphere":[140],"has":[141],"$$O(1/r^2)$$":[146],"<mml:math":[147],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[148],"<mml:mrow>":[149],"<mml:mi>O</mml:mi>":[150],"<mml:mo>(</mml:mo>":[151],"<mml:mn>1</mml:mn>":[152],"<mml:mo>/</mml:mo>":[153],"<mml:msup>":[154],"<mml:mi>r</mml:mi>":[155],"<mml:mn>2</mml:mn>":[156],"</mml:msup>":[157],"<mml:mo>)</mml:mo>":[158],"</mml:mrow>":[159],"</mml:math>":[160],".":[161],"Moreover,":[162],"show":[164],"RLT-relaxation":[168],"generalization":[171],"minimizing":[176],"forms":[177],"degree":[179],"d":[180],"simplex,":[183],"De":[186],"Klerk":[187],"et":[188],"al.":[189],"(J":[190],"Theor":[191],"Comput":[192],"Sci":[193],"361(2\u20133):210\u2013225,":[194],"2006).":[195]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-04T08:30:34.212998","created_date":"2022-07-22T00:00:00"}