{"id":"https://openalex.org/W2112086696","doi":"https://doi.org/10.1007/s10898-015-0313-4","title":"Spectrahedral cones generated by rank 1 matrices","display_name":"Spectrahedral cones generated by rank 1 matrices","publication_year":2015,"publication_date":"2015-06-06","ids":{"openalex":"https://openalex.org/W2112086696","doi":"https://doi.org/10.1007/s10898-015-0313-4","mag":"2112086696"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-015-0313-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-015-0313-4","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1409.4781","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045144923","display_name":"Roland Hildebrand","orcid":"https://orcid.org/0000-0002-4418-8514"},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Roland Hildebrand","raw_affiliation_strings":["WIAS, Mohrenstrasse 39, 10117, Berlin, Germany","Weierstrass Institute [Berlin] (Mohrenstra\u00dfe 39, 10117 Berlin - Germany)","DAO - Donn\u00e9es, Apprentissage et Optimisation (France)"],"affiliations":[{"raw_affiliation_string":"WIAS, Mohrenstrasse 39, 10117, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]},{"raw_affiliation_string":"Weierstrass Institute [Berlin] (Mohrenstra\u00dfe 39, 10117 Berlin - Germany)","institution_ids":["https://openalex.org/I4210092021"]},{"raw_affiliation_string":"DAO - Donn\u00e9es, Apprentissage et Optimisation (France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045144923"],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":1.0093,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.7578635,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"64","issue":"2","first_page":"349","last_page":"397"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9988999962806702,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9911999702453613,"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/cone","display_name":"Cone (formal languages)","score":0.7941245436668396},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6878794431686401},{"id":"https://openalex.org/keywords/convex-cone","display_name":"Convex cone","score":0.6845272779464722},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6725031137466431},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.6547558903694153},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6403310298919678},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5785465240478516},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5595114827156067},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.49499648809432983},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.4925990700721741},{"id":"https://openalex.org/keywords/quadratic-form","display_name":"Quadratic form (statistics)","score":0.45515531301498413},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4443019926548004},{"id":"https://openalex.org/keywords/dual-cone-and-polar-cone","display_name":"Dual cone and polar cone","score":0.4346987009048462},{"id":"https://openalex.org/keywords/linear-space","display_name":"Linear space","score":0.42827939987182617},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.34837794303894043},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30089545249938965},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.18861061334609985},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.18356889486312866},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17643049359321594},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13657596707344055},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13527613878250122},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10180386900901794},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.08283823728561401}],"concepts":[{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.7941245436668396},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6878794431686401},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.6845272779464722},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6725031137466431},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.6547558903694153},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6403310298919678},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5785465240478516},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5595114827156067},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.49499648809432983},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.4925990700721741},{"id":"https://openalex.org/C152022596","wikidata":"https://www.wikidata.org/wiki/Q7268361","display_name":"Quadratic form (statistics)","level":2,"score":0.45515531301498413},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4443019926548004},{"id":"https://openalex.org/C24484764","wikidata":"https://www.wikidata.org/wiki/Q2687694","display_name":"Dual cone and polar cone","level":3,"score":0.4346987009048462},{"id":"https://openalex.org/C176370821","wikidata":"https://www.wikidata.org/wiki/Q1826459","display_name":"Linear space","level":2,"score":0.42827939987182617},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.34837794303894043},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30089545249938965},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.18861061334609985},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.18356889486312866},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17643049359321594},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13657596707344055},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13527613878250122},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10180386900901794},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.08283823728561401},{"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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10898-015-0313-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-015-0313-4","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1409.4781","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1409.4781","pdf_url":"https://arxiv.org/pdf/1409.4781","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:HAL:hal-01417475v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01417475","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Global Optimization, 2016, 64 (2), pp.349-397. ⟨10.1007/s10898-015-0313-4⟩","raw_type":"Journal articles"},{"id":"pmh:oai:RePEc:spr:jglopt:v:64:y:2016:i:2:d:10.1007_s10898-015-0313-4","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-015-0313-4","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":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1409.4781","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1409.4781","pdf_url":"https://arxiv.org/pdf/1409.4781","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":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2112086696.pdf","grobid_xml":"https://content.openalex.org/works/W2112086696.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1522799773","https://openalex.org/W1806104592","https://openalex.org/W1985123706","https://openalex.org/W1996215314","https://openalex.org/W2011039300","https://openalex.org/W2018501141","https://openalex.org/W2025202934","https://openalex.org/W2034769312","https://openalex.org/W2047386668","https://openalex.org/W2055985383","https://openalex.org/W2059035181","https://openalex.org/W2060941833","https://openalex.org/W2061269184","https://openalex.org/W2065053468","https://openalex.org/W2065706751","https://openalex.org/W2084407118","https://openalex.org/W2085784518","https://openalex.org/W2091109213","https://openalex.org/W2119340035","https://openalex.org/W2142398091","https://openalex.org/W2575222505","https://openalex.org/W3144358832","https://openalex.org/W3148554666","https://openalex.org/W4233252806","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1991975655","https://openalex.org/W1971414685","https://openalex.org/W2068531293","https://openalex.org/W1974329054","https://openalex.org/W2069365182","https://openalex.org/W2008469348","https://openalex.org/W2896003473","https://openalex.org/W1599513139","https://openalex.org/W2007281837","https://openalex.org/W2029590768"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}