{"id":"https://openalex.org/W1852756082","doi":"https://doi.org/10.1080/10556788.2015.1052969","title":"Perturbed sums-of-squares theorem for polynomial optimization and its applications","display_name":"Perturbed sums-of-squares theorem for polynomial optimization and its applications","publication_year":2015,"publication_date":"2015-06-16","ids":{"openalex":"https://openalex.org/W1852756082","doi":"https://doi.org/10.1080/10556788.2015.1052969","mag":"1852756082"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2015.1052969","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2015.1052969","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1304.0065","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113934718","display_name":"Masakazu Muramatsu","orcid":null},"institutions":[{"id":"https://openalex.org/I20529979","display_name":"University of Electro-Communications","ror":"https://ror.org/02x73b849","country_code":"JP","type":"education","lineage":["https://openalex.org/I20529979"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masakazu Muramatsu","raw_affiliation_strings":["Department of Communication Engineering and Informatics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan","Department of Communication Engineering and Informatics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo182-8585, Japan#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Communication Engineering and Informatics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan","institution_ids":["https://openalex.org/I20529979"]},{"raw_affiliation_string":"Department of Communication Engineering and Informatics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo182-8585, Japan#TAB#","institution_ids":["https://openalex.org/I20529979"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080255628","display_name":"Hayato Waki","orcid":"https://orcid.org/0000-0002-0531-2201"},"institutions":[{"id":"https://openalex.org/I135598925","display_name":"Kyushu University","ror":"https://ror.org/00p4k0j84","country_code":"JP","type":"education","lineage":["https://openalex.org/I135598925"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hayato Waki","raw_affiliation_strings":["Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan","Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka819-0395, Japan#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan","institution_ids":["https://openalex.org/I135598925"]},{"raw_affiliation_string":"Institute of Mathematics for Industry, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka819-0395, Japan#TAB#","institution_ids":["https://openalex.org/I135598925"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062941227","display_name":"Levent Tun\u00e7el","orcid":"https://orcid.org/0000-0001-5071-216X"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Levent Tun\u00e7el","raw_affiliation_strings":["Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1","Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, CanadaN2L 3G1#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1","institution_ids":["https://openalex.org/I151746483"]},{"raw_affiliation_string":"Department of Combinatorics and Optimization, Faculty of Mathematics, University of Waterloo, Waterloo, Ontario, CanadaN2L 3G1#TAB#","institution_ids":["https://openalex.org/I151746483"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5113934718"],"corresponding_institution_ids":["https://openalex.org/I20529979"],"apc_list":null,"apc_paid":null,"fwci":0.5061,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.63520408,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"31","issue":"1","first_page":"134","last_page":"156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9954000115394592,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9746999740600586,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8618740439414978},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.6847702264785767},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.6568728089332581},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5760447978973389},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5734075903892517},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5329476594924927},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4379134178161621},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4350129961967468},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4041002094745636},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36900725960731506},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35802948474884033},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.31456583738327026},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15221551060676575}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8618740439414978},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.6847702264785767},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6568728089332581},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5760447978973389},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5734075903892517},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5329476594924927},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4379134178161621},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4350129961967468},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4041002094745636},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36900725960731506},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35802948474884033},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.31456583738327026},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15221551060676575},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1080/10556788.2015.1052969","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2015.1052969","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1304.0065","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.0065","pdf_url":"https://arxiv.org/pdf/1304.0065","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":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.308.7205","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.308.7205","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uwaterloo.ca/~ltuncel/publications/arxivMWT2013.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.638.7722","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.638.7722","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uwaterloo.ca/~ltuncel/publications/arxivMWT2013.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.770.7057","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.770.7057","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1304.0065.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1304.0065","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1304.0065","pdf_url":"https://arxiv.org/pdf/1304.0065","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G840661538","display_name":null,"funder_award_id":"19560063,22740056,26330025,26400203","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W10800830","https://openalex.org/W272958077","https://openalex.org/W1566177854","https://openalex.org/W1605206672","https://openalex.org/W1734843296","https://openalex.org/W1904611021","https://openalex.org/W1967073510","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1986699627","https://openalex.org/W1989190791","https://openalex.org/W1992008263","https://openalex.org/W1998648277","https://openalex.org/W2000893969","https://openalex.org/W2000923338","https://openalex.org/W2001098796","https://openalex.org/W2009009651","https://openalex.org/W2011603435","https://openalex.org/W2049225870","https://openalex.org/W2054413257","https://openalex.org/W2060533249","https://openalex.org/W2066459185","https://openalex.org/W2066736759","https://openalex.org/W2071143636","https://openalex.org/W2071550336","https://openalex.org/W2080359169","https://openalex.org/W2083546432","https://openalex.org/W2085045434","https://openalex.org/W2091288499","https://openalex.org/W2104296611","https://openalex.org/W2165281529","https://openalex.org/W2166798101","https://openalex.org/W2498144272","https://openalex.org/W2519172631","https://openalex.org/W3101866124","https://openalex.org/W4244999758"],"related_works":["https://openalex.org/W2493494838","https://openalex.org/W2963700124","https://openalex.org/W2624196447","https://openalex.org/W2077924482","https://openalex.org/W4297923520","https://openalex.org/W2771160919","https://openalex.org/W4301659259","https://openalex.org/W4298028631","https://openalex.org/W1571037741","https://openalex.org/W2762005921"],"abstract_inverted_index":{"We":[0,60,98],"consider":[1],"a":[2,8,12,18],"property":[3,24],"of":[4,30,57,70,77,88,105],"positive":[5],"polynomials":[6],"on":[7,68],"compact":[9],"set":[10],"with":[11,37],"small":[13],"perturbation.":[14],"When":[15],"applied":[16],"to":[17],"polynomial":[19],"optimization":[20],"problem":[21],"(POP),":[22],"the":[23,27,31,54,58,103],"implies":[25],"that":[26,82],"optimal":[28,55],"value":[29,56],"corresponding":[32],"SemiDefinite":[33],"Programming":[34],"(SDP)":[35],"relaxation":[36,40],"sufficiently":[38],"large":[39],"order":[41],"is":[42,53,81],"bounded":[43],"from":[44,48],"below":[45],"by":[46,50,96],"and":[47,102],"above":[49],",":[51],"where":[52],"POP.":[59],"propose":[61],"new":[62],"SDP":[63,79],"relaxations":[64,80],"for":[65],"POP":[66],"based":[67],"modifications":[69],"existing":[71],"sums-of-squares":[72],"representation":[73],"theorems.":[74],"An":[75],"advantage":[76],"our":[78,106],"in":[83],"many":[84],"cases":[85],"they":[86],"are":[87],"considerably":[89],"smaller":[90],"dimension":[91],"than":[92],"those":[93],"originally":[94],"proposed":[95],"Lasserre.":[97],"present":[99],"some":[100],"applications":[101],"results":[104],"computational":[107],"experiments.":[108]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
