{"id":"https://openalex.org/W2088822215","doi":"https://doi.org/10.1007/s10589-012-9513-8","title":"Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials","display_name":"Algorithmic aspects of sums of Hermitian squares of noncommutative polynomials","publication_year":2012,"publication_date":"2012-10-24","ids":{"openalex":"https://openalex.org/W2088822215","doi":"https://doi.org/10.1007/s10589-012-9513-8","mag":"2088822215"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-012-9513-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-012-9513-8","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/189201","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109393302","display_name":"Sabine Burgdorf","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Sabine Burgdorf","raw_affiliation_strings":["SB-MATHGEOM-EGG, EPFL, 1015, Lausanne, Switzerland","SB-MATHGEOM-EGG, EPFL, Lausanne, Switzerland 1015"],"affiliations":[{"raw_affiliation_string":"SB-MATHGEOM-EGG, EPFL, 1015, Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]},{"raw_affiliation_string":"SB-MATHGEOM-EGG, EPFL, Lausanne, Switzerland 1015","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053003807","display_name":"Kristijan Cafuta","orcid":null},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Kristijan Cafuta","raw_affiliation_strings":["Fakulteta za elektrotehniko, Laboratorij za uporabno matematiko, Univerza v Ljubljani, Tr\u017ea\u0161ka 25, 1000, Ljubljana, Slovenia","Fakulteta za elektrotehniko, Laboratorij za uporabno matematiko, Univerza v Ljubljani, Ljubljana, Slovenia 1000#TAB#"],"affiliations":[{"raw_affiliation_string":"Fakulteta za elektrotehniko, Laboratorij za uporabno matematiko, Univerza v Ljubljani, Tr\u017ea\u0161ka 25, 1000, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]},{"raw_affiliation_string":"Fakulteta za elektrotehniko, Laboratorij za uporabno matematiko, Univerza v Ljubljani, Ljubljana, Slovenia 1000#TAB#","institution_ids":["https://openalex.org/I153976015"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065891534","display_name":"Igor Klep","orcid":"https://orcid.org/0000-0001-5245-8484"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Igor Klep","raw_affiliation_strings":["Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand","Department of Mathematics, The University of Auckland, Auckland, New Zealand 1142"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"Department of Mathematics, The University of Auckland, Auckland, New Zealand 1142","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074212676","display_name":"Janez Povh","orcid":"https://orcid.org/0000-0002-9856-1476"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Janez Povh","raw_affiliation_strings":["Fakulteta za informacijske \u0161tudije v Novem mestu, Novi trg 5, 8000, Novo mesto, Slovenia","Fakulteta za informacijske \u0161tudije v Novem mestu, Novo mesto, Slovenia 8000#TAB#"],"affiliations":[{"raw_affiliation_string":"Fakulteta za informacijske \u0161tudije v Novem mestu, Novi trg 5, 8000, Novo mesto, Slovenia","institution_ids":[]},{"raw_affiliation_string":"Fakulteta za informacijske \u0161tudije v Novem mestu, Novo mesto, Slovenia 8000#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5109393302"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.4482,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66058394,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"55","issue":"1","first_page":"137","last_page":"153"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9980000257492065,"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/hermitian-matrix","display_name":"Hermitian matrix","score":0.8541027307510376},{"id":"https://openalex.org/keywords/noncommutative-geometry","display_name":"Noncommutative geometry","score":0.848634660243988},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8279257416725159},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.5877007246017456},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.5790573358535767},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4833330810070038},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46857714653015137},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4337940812110901},{"id":"https://openalex.org/keywords/explained-sum-of-squares","display_name":"Explained sum of squares","score":0.4206579327583313},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3396528363227844},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28220468759536743},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.2604794502258301},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.22380885481834412}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.8541027307510376},{"id":"https://openalex.org/C68797384","wikidata":"https://www.wikidata.org/wiki/Q2746792","display_name":"Noncommutative geometry","level":2,"score":0.848634660243988},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8279257416725159},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.5877007246017456},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.5790573358535767},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4833330810070038},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46857714653015137},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4337940812110901},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.4206579327583313},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3396528363227844},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28220468759536743},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2604794502258301},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.22380885481834412},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10589-012-9513-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-012-9513-8","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.416.543","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.416.543","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.optimization-online.org/DB_FILE/2011/12/3258.pdf","raw_type":"text"},{"id":"pmh:oai:RePEc:spr:coopap:v:55:y:2013:i:1:p:137-153","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s10589-012-9513-8","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":"article"},{"id":"pmh:oai:infoscience.epfl.ch:189201","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/189201","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:189201","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/189201","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W126279018","https://openalex.org/W162681849","https://openalex.org/W1540295818","https://openalex.org/W1549638383","https://openalex.org/W1559197676","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1977327182","https://openalex.org/W1993000710","https://openalex.org/W1995320256","https://openalex.org/W1996541174","https://openalex.org/W2000320746","https://openalex.org/W2003733377","https://openalex.org/W2004538321","https://openalex.org/W2016389104","https://openalex.org/W2025522466","https://openalex.org/W2040499718","https://openalex.org/W2046866204","https://openalex.org/W2057445306","https://openalex.org/W2064609151","https://openalex.org/W2065791599","https://openalex.org/W2066978207","https://openalex.org/W2085729541","https://openalex.org/W2096750502","https://openalex.org/W2118550318","https://openalex.org/W2150044500","https://openalex.org/W2170693128","https://openalex.org/W2259770606","https://openalex.org/W2328912295","https://openalex.org/W2495457432","https://openalex.org/W2912522929","https://openalex.org/W2962725330","https://openalex.org/W3105661328","https://openalex.org/W4243539849"],"related_works":["https://openalex.org/W2333955266","https://openalex.org/W2015685619","https://openalex.org/W2090649758","https://openalex.org/W4249089511","https://openalex.org/W131110362","https://openalex.org/W2065791599","https://openalex.org/W2088822215","https://openalex.org/W600709054","https://openalex.org/W1664790483","https://openalex.org/W1649193690"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}