{"id":"https://openalex.org/W3132822607","doi":"https://doi.org/10.1007/s10107-023-01958-0","title":"Hyperbolicity cones are amenable","display_name":"Hyperbolicity cones are amenable","publication_year":2023,"publication_date":"2023-04-08","ids":{"openalex":"https://openalex.org/W3132822607","doi":"https://doi.org/10.1007/s10107-023-01958-0","mag":"3132822607"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-023-01958-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-023-01958-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-023-01958-0.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-023-01958-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005592247","display_name":"Bruno F. Louren\u00e7o","orcid":"https://orcid.org/0000-0003-2369-0107"},"institutions":[{"id":"https://openalex.org/I4210134673","display_name":"The Institute of Statistical Mathematics","ror":"https://ror.org/03jcejr58","country_code":"JP","type":"facility","lineage":["https://openalex.org/I1319490839","https://openalex.org/I4210134673","https://openalex.org/I4210158934"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Bruno F. Louren\u00e7o","raw_affiliation_strings":["Department of Statistical Inference and Mathematics, Institute of Statistical Mathematics, Tachikawa, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistical Inference and Mathematics, Institute of Statistical Mathematics, Tachikawa, Japan","institution_ids":["https://openalex.org/I4210134673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048369644","display_name":"Vera Roshchina","orcid":"https://orcid.org/0000-0002-8361-6876"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Vera Roshchina","raw_affiliation_strings":["School of Mathematics and Statistics, UNSW Sydney, Kensington, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, UNSW Sydney, Kensington, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5037774037","display_name":"James Saunderson","orcid":"https://orcid.org/0000-0002-5456-0180"},"institutions":[{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"James Saunderson","raw_affiliation_strings":["Department of Electrical and Computer Systems Engineering, Monash University, Melbourne, Australia"],"raw_orcid":"https://orcid.org/0000-0002-5456-0180","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Systems Engineering, Monash University, Melbourne, Australia","institution_ids":["https://openalex.org/I56590836"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037774037"],"corresponding_institution_ids":["https://openalex.org/I56590836"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":9.885,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.95597166,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"204","issue":"1-2","first_page":"753","last_page":"764"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T12170","display_name":"History and Theory of Mathematics","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.9804999828338623,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.965499997138977,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.8278002738952637},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7893195152282715},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.77858567237854},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6715033650398254},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5029715895652771},{"id":"https://openalex.org/keywords/convex-cone","display_name":"Convex cone","score":0.4904012680053711},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.47709187865257263},{"id":"https://openalex.org/keywords/dual-cone-and-polar-cone","display_name":"Dual cone and polar cone","score":0.4503445029258728},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.42139580845832825},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.24521368741989136},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2034519612789154},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.18812361359596252},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06808251142501831}],"concepts":[{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.8278002738952637},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7893195152282715},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.77858567237854},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6715033650398254},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5029715895652771},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.4904012680053711},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.47709187865257263},{"id":"https://openalex.org/C24484764","wikidata":"https://www.wikidata.org/wiki/Q2687694","display_name":"Dual cone and polar cone","level":3,"score":0.4503445029258728},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.42139580845832825},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.24521368741989136},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2034519612789154},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.18812361359596252},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06808251142501831},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-023-01958-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-023-01958-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-023-01958-0.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2102.06359","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.06359","pdf_url":"https://arxiv.org/pdf/2102.06359","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":"doi:10.1007/s10107-023-01958-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-023-01958-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-023-01958-0.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1395256119","display_name":"An optimisation-based framework for non-classical Chebyshev approximation","funder_award_id":"DP180100602","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G4758419248","display_name":"Solving ill-posed conic optimization problems","funder_award_id":"19K20217","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6101260676","display_name":"Realising the potential of hyperbolic programming","funder_award_id":"DE210101056","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G6366594956","display_name":"Geometry in projection methods and fixed-point theory","funder_award_id":"DP200100124","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G7005591275","display_name":"Geometry and Conditioning in Structured Conic Problems","funder_award_id":"DE150100240","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G7706312173","display_name":null,"funder_award_id":"9K20217","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8588626415","display_name":"Development of Optimization Mathematical Modeling","funder_award_id":"21H03398","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320315885","display_name":"Australian Government","ror":"https://ror.org/0314h5y94"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3132822607.pdf"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1482736558","https://openalex.org/W2015626260","https://openalex.org/W2025202934","https://openalex.org/W2073718737","https://openalex.org/W2075706482","https://openalex.org/W2080359169","https://openalex.org/W2087169144","https://openalex.org/W2152309892","https://openalex.org/W2153997639","https://openalex.org/W2317283549","https://openalex.org/W2778468193","https://openalex.org/W2963314387","https://openalex.org/W2986179863","https://openalex.org/W2992636988","https://openalex.org/W3089409253","https://openalex.org/W3101080484","https://openalex.org/W3106367349"],"related_works":["https://openalex.org/W2484043914","https://openalex.org/W2068531293","https://openalex.org/W1974329054","https://openalex.org/W2184361932","https://openalex.org/W1965358437","https://openalex.org/W1963700989","https://openalex.org/W2073718737","https://openalex.org/W2116190705","https://openalex.org/W2030016889","https://openalex.org/W2064755091"],"abstract_inverted_index":{"Abstract":[0],"Amenability":[1],"is":[2,12,57,87,111],"a":[3,34,84,88,92,106,112],"notion":[4],"of":[5,36,49,75,83,99],"facial":[6],"exposedness":[7],"for":[8],"convex":[9,40],"cones":[10,32,41,46,62,70],"that":[11,42,59,67,80,96],"stronger":[13,25],"than":[14,26],"being":[15,28],"facially":[16,29],"dual":[17],"complete":[18],"(or":[19],"\u2018nice\u2019)":[20],"which":[21],"is,":[22],"in":[23],"turn,":[24],"merely":[27],"exposed.":[30],"Hyperbolicity":[31],"are":[33,63,71],"family":[35],"algebraically":[37],"structured":[38],"closed":[39],"contain":[43],"all":[44,60,68],"spectrahedral":[45,61],"(linear":[47],"sections":[48],"positive":[50],"semidefinite":[51],"cones)":[52],"as":[53],"special":[54],"cases.":[55],"It":[56],"known":[58],"amenable.":[64,72],"We":[65],"establish":[66],"hyperbolicity":[69,85,89,101,113],"As":[73,91],"part":[74],"the":[76,97],"argument,":[77],"we":[78,94],"show":[79,95],"any":[81],"face":[82],"cone":[86],"cone.":[90,114],"corollary,":[93],"intersection":[98],"two":[100],"cones,":[102],"not":[103],"necessarily":[104],"sharing":[105],"common":[107],"relative":[108],"interior":[109],"point,":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}
