{"id":"https://openalex.org/W4401082852","doi":"https://doi.org/10.1080/10556788.2024.2339221","title":"Matrix extreme points and free extreme points of free spectrahedra","display_name":"Matrix extreme points and free extreme points of free spectrahedra","publication_year":2024,"publication_date":"2024-07-29","ids":{"openalex":"https://openalex.org/W4401082852","doi":"https://doi.org/10.1080/10556788.2024.2339221"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2024.2339221","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2024.2339221","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020522281","display_name":"Aidan Epperly","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aidan Epperly","raw_affiliation_strings":["Mathematics Department, UC San Diego, La Jolla, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, UC San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017164422","display_name":"Eric Evert","orcid":"https://orcid.org/0000-0002-5488-8725"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Eric Evert","raw_affiliation_strings":["Computer Science Department, Northwestern University, Evanston, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science Department, Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080005590","display_name":"J. William Helton","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. William Helton","raw_affiliation_strings":["Mathematics Department, UC San Diego, La Jolla, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, UC San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065891534","display_name":"Igor Klep","orcid":"https://orcid.org/0000-0001-5245-8484"},"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"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Igor Klep","raw_affiliation_strings":["Faculty of Mathematics and Physics, University of Ljubljana &amp; Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Physics, University of Ljubljana &amp; Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015","https://openalex.org/I4210106342"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5017164422"],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12484462,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"6","first_page":"1263","last_page":"1308"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9958000183105469,"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/T11673","display_name":"Advanced Topics in Algebra","score":0.9850000143051147,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/extreme-point","display_name":"Extreme point","score":0.8565233945846558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7604368329048157},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.591014564037323},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5713866353034973},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.494219571352005},{"id":"https://openalex.org/keywords/free-probability","display_name":"Free probability","score":0.48914650082588196},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.44268402457237244},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4198916256427765}],"concepts":[{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.8565233945846558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7604368329048157},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.591014564037323},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5713866353034973},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.494219571352005},{"id":"https://openalex.org/C70120467","wikidata":"https://www.wikidata.org/wiki/Q515893","display_name":"Free probability","level":2,"score":0.48914650082588196},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44268402457237244},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4198916256427765},{"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2024.2339221","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2024.2339221","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4025136288","display_name":null,"funder_award_id":"P1-0222 and grants J1-50002, J1-2453, N1-0217, J1-3004","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W31148203","https://openalex.org/W162681849","https://openalex.org/W653291882","https://openalex.org/W1494452888","https://openalex.org/W1523764298","https://openalex.org/W1566904297","https://openalex.org/W1602809669","https://openalex.org/W1777038420","https://openalex.org/W1884490694","https://openalex.org/W1978911250","https://openalex.org/W2000106536","https://openalex.org/W2000320746","https://openalex.org/W2026820086","https://openalex.org/W2048223511","https://openalex.org/W2057196459","https://openalex.org/W2065706751","https://openalex.org/W2080180674","https://openalex.org/W2080991235","https://openalex.org/W2088104180","https://openalex.org/W2114382532","https://openalex.org/W2127765692","https://openalex.org/W2132677492","https://openalex.org/W2269541633","https://openalex.org/W2271608424","https://openalex.org/W2331274486","https://openalex.org/W2476213965","https://openalex.org/W2525822570","https://openalex.org/W2533274535","https://openalex.org/W2560485006","https://openalex.org/W2744182242","https://openalex.org/W2747308942","https://openalex.org/W2795723564","https://openalex.org/W2811425173","https://openalex.org/W2962769465","https://openalex.org/W2963046447","https://openalex.org/W2963150178","https://openalex.org/W2963839924","https://openalex.org/W2964203077","https://openalex.org/W2964266156","https://openalex.org/W2996712557","https://openalex.org/W3047012223","https://openalex.org/W3099303613","https://openalex.org/W3099888093","https://openalex.org/W3101642943","https://openalex.org/W3105482478","https://openalex.org/W3105661328","https://openalex.org/W3105862776","https://openalex.org/W3106372671","https://openalex.org/W3106417306","https://openalex.org/W3119283627","https://openalex.org/W3134903385","https://openalex.org/W3179315625","https://openalex.org/W3183816071","https://openalex.org/W3195770928","https://openalex.org/W3210289813","https://openalex.org/W3216885398","https://openalex.org/W4210472623"],"related_works":["https://openalex.org/W3189643850","https://openalex.org/W2375407244","https://openalex.org/W2775221851","https://openalex.org/W2061565576","https://openalex.org/W2039994059","https://openalex.org/W1913561908","https://openalex.org/W2120254947","https://openalex.org/W2339216765","https://openalex.org/W3210319919","https://openalex.org/W3216885398"],"abstract_inverted_index":{"Free":[0,29],"spectrahedra":[1,30,52],"are":[2,19,31,53,94,149],"dimension":[3],"free":[4,47,51,78,122,127,151],"solution":[5],"sets":[6],"to":[7],"linear":[8],"matrix":[9,42,76,140,145],"inequalities":[10],"of":[11,41,50,66,91,117,120,126],"the":[12,15,23,39],"form":[13],"LA(X)=Id\u2297In+A1\u2297X1+A2\u2297X2+\u22ef+Ag\u2297Xg\u2ab00,where":[14],"Ai":[16],"and":[17,22,38,46,60,77,104,142],"Xi":[18,24],"symmetric":[20],"matrices":[21],"have":[25,74],"any":[26],"size":[27],"n\u00d7n.":[28],"ubiquitous":[32],"in":[33,124],"systems":[34],"engineering,":[35],"operator":[36],"algebras,":[37],"theory":[40],"convex":[43],"sets.":[44],"Matrix":[45],"extreme":[48,67,79,92,128,141,146],"points":[49,93,147],"particularly":[54],"important.":[55],"We":[56,130],"present":[57,103],"theoretical,":[58],"algorithmic,":[59],"experimental":[61],"results":[62],"illuminating":[63],"basic":[64],"properties":[65],"points.":[68,129],"For":[69],"example,":[70],"though":[71],"many":[72],"authors":[73],"studied":[75],"points,":[80],"it":[81],"has":[82],"until":[83],"now":[84],"been":[85],"unknown":[86],"if":[87,136],"these":[88],"two":[89],"types":[90],"actually":[95],"different.":[96],"This":[97],"paper":[98],"settles":[99],"that":[100,148],"issue.We":[101],"also":[102,131],"analyze":[105],"several":[106],"algorithms.":[107],"Namely,":[108],"we":[109],"perfect":[110],"an":[111,115,118],"algorithm":[112],"for":[113,134,143],"computing":[114,144],"expansion":[116],"element":[119],"a":[121,137],"spectrahedron":[123],"terms":[125],"give":[132],"algorithms":[133],"testing":[135],"point":[138],"is":[139],"not":[150],"extreme.":[152]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
