{"id":"https://openalex.org/W2911923979","doi":"https://doi.org/10.1137/19m1245670","title":"Limitations on the Expressive Power of Convex Cones without Long Chains of Faces","display_name":"Limitations on the Expressive Power of Convex Cones without Long Chains of Faces","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2911923979","doi":"https://doi.org/10.1137/19m1245670","mag":"2911923979"},"language":"en","primary_location":{"id":"doi:10.1137/19m1245670","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1245670","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1902.06401","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037774037","display_name":"James Saunderson","orcid":"https://orcid.org/0000-0002-5456-0180"},"institutions":[{"id":"https://openalex.org/I4210116219","display_name":"Engineering Systems (United States)","ror":"https://ror.org/02qg60849","country_code":"US","type":"company","lineage":["https://openalex.org/I4210116219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"James Saunderson","raw_affiliation_strings":["Electrical and Computer Systems Engineering"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Systems Engineering","institution_ids":["https://openalex.org/I4210116219"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037774037"],"corresponding_institution_ids":["https://openalex.org/I4210116219"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00768156,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"30","issue":"1","first_page":"1033","last_page":"1047"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9962999820709229,"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/conic-optimization","display_name":"Conic optimization","score":0.7744938135147095},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7126758098602295},{"id":"https://openalex.org/keywords/convex-cone","display_name":"Convex cone","score":0.7091578245162964},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.6791240572929382},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.6459898948669434},{"id":"https://openalex.org/keywords/dual-cone-and-polar-cone","display_name":"Dual cone and polar cone","score":0.49770238995552063},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4457116723060608},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40646296739578247},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3469861149787903},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3230588436126709},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.2933001220226288},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13529062271118164},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08914589881896973}],"concepts":[{"id":"https://openalex.org/C79187972","wikidata":"https://www.wikidata.org/wiki/Q2654791","display_name":"Conic optimization","level":5,"score":0.7744938135147095},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7126758098602295},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.7091578245162964},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.6791240572929382},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.6459898948669434},{"id":"https://openalex.org/C24484764","wikidata":"https://www.wikidata.org/wiki/Q2687694","display_name":"Dual cone and polar cone","level":3,"score":0.49770238995552063},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4457116723060608},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40646296739578247},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3469861149787903},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3230588436126709},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.2933001220226288},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13529062271118164},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08914589881896973}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/19m1245670","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1245670","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1902.06401","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.06401","pdf_url":"https://arxiv.org/pdf/1902.06401","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:circle.library.ubc.ca:2429/72384","is_oa":true,"landing_page_url":"http://hdl.handle.net/2429/72384","pdf_url":null,"source":{"id":"https://openalex.org/S4377196297","display_name":"cIRcle (University of British Columbia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I141945490","host_organization_name":"University of British Columbia","host_organization_lineage":["https://openalex.org/I141945490"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Moving Image"},{"id":"doi:10.48550/arxiv.1902.06401","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1902.06401","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.14288/1.0385848","is_oa":true,"landing_page_url":"https://doi.org/10.14288/1.0385848","pdf_url":null,"source":{"id":"https://openalex.org/S7407053062","display_name":"Open Collections","issn_l":null,"issn":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.5446/57961","is_oa":true,"landing_page_url":"https://doi.org/10.5446/57961","pdf_url":null,"source":{"id":"https://openalex.org/S7407052952","display_name":"TIB KMO / FLOWWORKS GmbH","issn_l":null,"issn":[],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:2911923979","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1902.06401","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1902.06401","pdf_url":"https://arxiv.org/pdf/1902.06401","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2911923979.pdf","grobid_xml":"https://content.openalex.org/works/W2911923979.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1568307856","https://openalex.org/W2006704773","https://openalex.org/W2034769312","https://openalex.org/W2035412546","https://openalex.org/W2039539620","https://openalex.org/W2065957732","https://openalex.org/W2077924482","https://openalex.org/W2078344584","https://openalex.org/W2095689360","https://openalex.org/W2133440210","https://openalex.org/W2138677859","https://openalex.org/W2152309892","https://openalex.org/W2158868635","https://openalex.org/W2166161233","https://openalex.org/W2239251014","https://openalex.org/W2317283549","https://openalex.org/W2512467472","https://openalex.org/W2536897863","https://openalex.org/W2620334136","https://openalex.org/W2963029052","https://openalex.org/W2963270550","https://openalex.org/W2963314387","https://openalex.org/W2963917343","https://openalex.org/W2963948022","https://openalex.org/W2964239200","https://openalex.org/W3123950972","https://openalex.org/W4206403023","https://openalex.org/W4292070118"],"related_works":["https://openalex.org/W2952895455","https://openalex.org/W3014980195","https://openalex.org/W2982274371","https://openalex.org/W2901353547","https://openalex.org/W3160355202","https://openalex.org/W3100992911","https://openalex.org/W1974329054","https://openalex.org/W2395691737","https://openalex.org/W246435646","https://openalex.org/W2061465245","https://openalex.org/W2069140866","https://openalex.org/W793094708","https://openalex.org/W2189286193","https://openalex.org/W2038334003","https://openalex.org/W2140964741","https://openalex.org/W2608920055","https://openalex.org/W2035036358","https://openalex.org/W3096811688","https://openalex.org/W3088114394","https://openalex.org/W1563732294"],"abstract_inverted_index":{"A":[0],"convex":[1,17,91,109],"optimization":[2],"problem":[3],"in":[4,51,56],"conic":[5,32,41],"form":[6],"involves":[7],"minimizing":[8],"a":[9,16,31,35,39,69,90,94,99,108,112,121,125,141],"linear":[10],"functional":[11],"over":[12],"the":[13,65,172,175,200],"intersection":[14],"of":[15,72,128,131,137,143,146,164,168,174,193,209],"cone":[18,45,67,92,110],"and":[19,203],"an":[20],"affine":[21],"subspace.":[22],"In":[23],"some":[24,52],"cases,":[25],"it":[26,117],"is":[27,47,63,68,140,178],"possible":[28],"to":[29,89,183],"replace":[30],"formulation":[33,42],"using":[34,43,124,162,191],"certain":[36,113],"cone,":[37,202],"with":[38,97],"\u201clifted\u201d":[40],"another":[44],"that":[46,106,179],"higher-dimensional,":[48],"but":[49],"simpler,":[50],"sense.":[53],"One":[54],"situation":[55],"which":[57,132,157],"this":[58],"can":[59],"be":[60],"computationally":[61],"advantageous":[62],"when":[64],"higher-dimensional":[66],"Cartesian":[70],"product":[71,100,127],"many":[73],"\u201clow-complexity\u201d":[74,194],"cones,":[75,79,129,195,199],"such":[76,98,196],"as":[77,197],"second-order":[78],"or":[80],"small":[81],"positive":[82,165],"semidefinite":[83,166],"cones.":[84],"This":[85,139],"paper":[86],"studies":[87],"obstructions":[88],"having":[93],"lifted":[95,122,160,189],"representation":[96,123],"structure.":[101],"The":[102],"main":[103,176],"result":[104,177],"says":[105],"whenever":[107],"has":[111,133],"neighborliness":[114],"property,":[115],"then":[116],"does":[118],"not":[119,187],"have":[120,188],"finite":[126],"each":[130],"only":[134,159],"short":[135],"chains":[136],"faces.":[138],"generalization":[142],"recent":[144],"work":[145],"Averkov":[147],"[SIAM":[148],"J.":[149],"Appl.":[150],"Alg.":[151],"Geom.,":[152],"3":[153],"(2019),":[154],"pp.":[155],"128--151],":[156],"considers":[158],"representations":[161,190],"products":[163,192],"cones":[167,181,204],"bounded":[169],"size.":[170],"Among":[171],"consequences":[173],"various":[180],"related":[182],"nonnegative":[184],"polynomials":[185,208],"do":[186],"smooth":[198],"exponential":[201],"defined":[205],"by":[206],"hyperbolic":[207],"low":[210],"degree.":[211]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
