{"id":"https://openalex.org/W2525822570","doi":"https://doi.org/10.1137/16m1100642","title":"Spectrahedral Containment and Operator Systems with Finite-Dimensional Realization","display_name":"Spectrahedral Containment and Operator Systems with Finite-Dimensional Realization","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2525822570","doi":"https://doi.org/10.1137/16m1100642","mag":"2525822570"},"language":"en","primary_location":{"id":"doi:10.1137/16m1100642","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1100642","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1100642","source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1100642","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017876886","display_name":"T. A. Fritz","orcid":"https://orcid.org/0000-0001-7081-2635"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tobias Fritz","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, Leipzig 04103, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, Leipzig 04103, Germany","institution_ids":["https://openalex.org/I4210091327","https://openalex.org/I4210119712"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037710247","display_name":"Tim Netzer","orcid":"https://orcid.org/0000-0002-7000-6200"},"institutions":[{"id":"https://openalex.org/I190249584","display_name":"Universit\u00e4t Innsbruck","ror":"https://ror.org/054pv6659","country_code":"AT","type":"education","lineage":["https://openalex.org/I190249584"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Tim Netzer","raw_affiliation_strings":["Universitt Innsbruck, Innsbruck 6020, Austria","Universit\u00e4t Innsbruck, Innsbruck 6020, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitt Innsbruck, Innsbruck 6020, Austria","institution_ids":["https://openalex.org/I190249584"]},{"raw_affiliation_string":"Universit\u00e4t Innsbruck, Innsbruck 6020, Austria","institution_ids":["https://openalex.org/I190249584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010043767","display_name":"Andreas Thom","orcid":"https://orcid.org/0000-0002-7245-2861"},"institutions":[{"id":"https://openalex.org/I78650965","display_name":"Technische Universit\u00e4t Dresden","ror":"https://ror.org/042aqky30","country_code":"DE","type":"education","lineage":["https://openalex.org/I78650965"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Thom","raw_affiliation_strings":["TU Dresden, Dresden 01062, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TU Dresden, Dresden 01062, Germany","institution_ids":["https://openalex.org/I78650965"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8239,"has_fulltext":true,"cited_by_count":40,"citation_normalized_percentile":{"value":0.9414271,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"1","issue":"1","first_page":"556","last_page":"574"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9965000152587891,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9965000152587891,"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":0.9889000058174133,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9876000285148621,"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/convexity","display_name":"Convexity","score":0.8077913522720337},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.8067829012870789},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6457451581954956},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.6271427273750305},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.5991507768630981},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.5736690759658813},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5724821090698242},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.5006396770477295},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4827808439731598},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.42751598358154297},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4232287108898163},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4156806468963623},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.40241825580596924},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3784193992614746},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32203274965286255},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2651880383491516},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.25884121656417847},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.17802312970161438}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8077913522720337},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.8067829012870789},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6457451581954956},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.6271427273750305},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.5991507768630981},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.5736690759658813},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5724821090698242},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5006396770477295},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4827808439731598},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.42751598358154297},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4232287108898163},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4156806468963623},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.40241825580596924},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3784193992614746},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32203274965286255},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2651880383491516},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25884121656417847},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17802312970161438},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1100642","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1100642","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1100642","source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1609.07908","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.07908","pdf_url":"https://arxiv.org/pdf/1609.07908","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:edoc.mpg.de:741480","is_oa":false,"landing_page_url":"http://edoc.mpg.de/741480","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"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":"SIAM Journal on Applied Algebra and Geometry, v.1, 556-574 (2017)","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1137/16m1100642","is_oa":true,"landing_page_url":"https://doi.org/10.1137/16m1100642","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/16M1100642","source":{"id":"https://openalex.org/S2996807011","display_name":"SIAM Journal on Applied Algebra and Geometry","issn_l":"2470-6566","issn":["2470-6566"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Algebra and Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3148599713","display_name":null,"funder_award_id":"P 29496-N35","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4605090208","display_name":"Groups, Dynamics, and Approximation","funder_award_id":"681207","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G6741834740","display_name":null,"funder_award_id":"681207","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G7161006176","display_name":null,"funder_award_id":"277728","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G7438906723","display_name":null,"funder_award_id":"277728","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2525822570.pdf","grobid_xml":"https://content.openalex.org/works/W2525822570.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W121267321","https://openalex.org/W653291882","https://openalex.org/W1523764298","https://openalex.org/W1596891174","https://openalex.org/W1602420091","https://openalex.org/W1655429119","https://openalex.org/W1777038420","https://openalex.org/W1966569916","https://openalex.org/W1967073510","https://openalex.org/W1968623066","https://openalex.org/W1973533265","https://openalex.org/W1973930360","https://openalex.org/W2027909800","https://openalex.org/W2048223511","https://openalex.org/W2065706751","https://openalex.org/W2086083500","https://openalex.org/W2088104180","https://openalex.org/W2106097701","https://openalex.org/W2116102644","https://openalex.org/W2127765692","https://openalex.org/W2204983263","https://openalex.org/W2269541633","https://openalex.org/W2331274486","https://openalex.org/W2495457432","https://openalex.org/W2952417687","https://openalex.org/W2962695108","https://openalex.org/W2963046447","https://openalex.org/W2963150178","https://openalex.org/W3102970043","https://openalex.org/W3105862776","https://openalex.org/W3106198068","https://openalex.org/W3106417306","https://openalex.org/W4241014687"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W940482830","https://openalex.org/W1642182499","https://openalex.org/W4286870264","https://openalex.org/W2279275934","https://openalex.org/W4304687059","https://openalex.org/W4242784854","https://openalex.org/W2963235221","https://openalex.org/W4280542881","https://openalex.org/W4384575929"],"abstract_inverted_index":{"Containment":[0],"problems":[1],"for":[2],"polytopes":[3],"and":[4,13,18,36,68,107,136],"spectrahedra":[5],"appear":[6],"in":[7,98,131],"various":[8,141],"applications,":[9],"such":[10],"as":[11],"linear":[12],"semidefinite":[14],"programming,":[15],"combinatorics,":[16],"convexity,":[17],"stability":[19],"analysis":[20],"of":[21,30,50,93,120,123],"differential":[22],"equations.":[23],"This":[24,116],"paper":[25],"explores":[26],"the":[27,51,91,102,110,121,124,132],"theoretical":[28],"background":[29],"a":[31,48,73,94,114],"method":[32,46],"proposed":[33],"by":[34,140],"Ben-Tal":[35],"Nemirovski":[37],"[SIAM":[38],"J.":[39],"Optim.,":[40],"12":[41],"(2002),":[42],"pp.":[43],"811--833].":[44],"Their":[45],"provides":[47],"strengthening":[49,103],"containment":[52],"problem,":[53],"which":[54],"is":[55,104,113,117],"algorithmically":[56],"well":[57],"tractable.":[58],"To":[59],"analyze":[60],"this":[61],"method,":[62],"we":[63],"study":[64],"abstract":[65],"operator":[66],"systems":[67],"investigate":[69],"when":[70,89],"they":[71],"have":[72],"finite-dimensional":[74],"concrete":[75],"realization.":[76],"Our":[77],"results":[78,139],"give":[79],"some":[80],"profound":[81],"insight":[82],"into":[83],"their":[84],"approach.":[85],"They":[86],"imply":[87],"that":[88],"testing":[90],"inclusion":[92],"fixed":[95],"polyhedral":[96,111],"cone":[97,112],"an":[99],"arbitrary":[100],"spectrahedron,":[101],"tight":[105],"if":[106,109],"only":[108],"simplex.":[115],"true":[118],"independent":[119],"representation":[122],"polytope.":[125],"We":[126],"also":[127],"deduce":[128],"error":[129],"bounds":[130],"other":[133],"cases,":[134],"simplifying":[135],"extending":[137],"recent":[138],"authors.":[142]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-10-07T00:00:00"}