{"id":"https://openalex.org/W2015144913","doi":"https://doi.org/10.1007/s10107-011-0457-z","title":"A convex polynomial that is not sos-convex","display_name":"A convex polynomial that is not sos-convex","publication_year":2011,"publication_date":"2011-06-01","ids":{"openalex":"https://openalex.org/W2015144913","doi":"https://doi.org/10.1007/s10107-011-0457-z","mag":"2015144913"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-011-0457-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-011-0457-z","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0903.1287","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Amir Ali Ahmadi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Amir Ali Ahmadi","raw_affiliation_strings":["Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":null,"display_name":"Pablo A. Parrilo","orcid":null},"institutions":[{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pablo A. Parrilo","raw_affiliation_strings":["Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":5.5069,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.95505376,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"135","issue":"1-2","first_page":"275","last_page":"292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.8698999881744385,"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":0.8698999881744385,"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":0.06639999896287918,"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":0.018799999728798866,"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/matrix-polynomial","display_name":"Matrix polynomial","score":0.7475000023841858},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7164999842643738},{"id":"https://openalex.org/keywords/homogeneous-polynomial","display_name":"Homogeneous polynomial","score":0.6419000029563904},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.6126000285148621},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5924000144004822},{"id":"https://openalex.org/keywords/stable-polynomial","display_name":"Stable polynomial","score":0.5823000073432922},{"id":"https://openalex.org/keywords/polynomial-matrix","display_name":"Polynomial matrix","score":0.5340999960899353},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4893999993801117},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.42649999260902405},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4032999873161316}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8633999824523926},{"id":"https://openalex.org/C101044782","wikidata":"https://www.wikidata.org/wiki/Q6787887","display_name":"Matrix polynomial","level":3,"score":0.7475000023841858},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7164999842643738},{"id":"https://openalex.org/C17103678","wikidata":"https://www.wikidata.org/wiki/Q1474074","display_name":"Homogeneous polynomial","level":4,"score":0.6419000029563904},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6126000285148621},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5924000144004822},{"id":"https://openalex.org/C45025165","wikidata":"https://www.wikidata.org/wiki/Q13424738","display_name":"Stable polynomial","level":5,"score":0.5823000073432922},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5370000004768372},{"id":"https://openalex.org/C126352355","wikidata":"https://www.wikidata.org/wiki/Q2562273","display_name":"Polynomial matrix","level":4,"score":0.5340999960899353},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4893999993801117},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.42649999260902405},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4032999873161316},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.3756999969482422},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3668000102043152},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.36320000886917114},{"id":"https://openalex.org/C170907076","wikidata":"https://www.wikidata.org/wiki/Q2613931","display_name":"Wilkinson's polynomial","level":5,"score":0.36239999532699585},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.3580999970436096},{"id":"https://openalex.org/C101525915","wikidata":"https://www.wikidata.org/wiki/Q7581979","display_name":"Square-free polynomial","level":4,"score":0.3529999852180481},{"id":"https://openalex.org/C30597210","wikidata":"https://www.wikidata.org/wiki/Q1163608","display_name":"Minimal polynomial (linear algebra)","level":5,"score":0.3499999940395355},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.34060001373291016},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.3208000063896179},{"id":"https://openalex.org/C97395012","wikidata":"https://www.wikidata.org/wiki/Q1422356","display_name":"Reciprocal polynomial","level":4,"score":0.31679999828338623},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3068000078201294},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.302700012922287},{"id":"https://openalex.org/C170412648","wikidata":"https://www.wikidata.org/wiki/Q4736415","display_name":"Alternating polynomial","level":4,"score":0.3003999888896942},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.296999990940094},{"id":"https://openalex.org/C2778265155","wikidata":"https://www.wikidata.org/wiki/Q7233276","display_name":"Positive definiteness","level":4,"score":0.2946000099182129},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.2921000123023987},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2750000059604645},{"id":"https://openalex.org/C42321380","wikidata":"https://www.wikidata.org/wiki/Q849705","display_name":"Characteristic polynomial","level":3,"score":0.26440000534057617},{"id":"https://openalex.org/C173047080","wikidata":"https://www.wikidata.org/wiki/Q6400676","display_name":"Kharitonov's theorem","level":5,"score":0.2565000057220459},{"id":"https://openalex.org/C52153879","wikidata":"https://www.wikidata.org/wiki/Q930499","display_name":"Symmetric polynomial","level":4,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-011-0457-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-011-0457-z","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0903.1287","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0903.1287","pdf_url":"https://arxiv.org/pdf/0903.1287","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0903.1287","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0903.1287","pdf_url":"https://arxiv.org/pdf/0903.1287","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1591868040","https://openalex.org/W1967184028","https://openalex.org/W1970515840","https://openalex.org/W1970556775","https://openalex.org/W1974962384","https://openalex.org/W1992374619","https://openalex.org/W1995320256","https://openalex.org/W1995488855","https://openalex.org/W2026578200","https://openalex.org/W2028123920","https://openalex.org/W2055993677","https://openalex.org/W2062200659","https://openalex.org/W2071040500","https://openalex.org/W2079135578","https://openalex.org/W2103764200","https://openalex.org/W2144748195","https://openalex.org/W2149179701","https://openalex.org/W2325692311","https://openalex.org/W2498847617","https://openalex.org/W2536620281","https://openalex.org/W2912522929","https://openalex.org/W2962725330","https://openalex.org/W4233252806","https://openalex.org/W4249667877","https://openalex.org/W4250589301","https://openalex.org/W6604321698","https://openalex.org/W6811264906"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":5}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2016-06-24T00:00:00"}