{"id":"https://openalex.org/W2922236301","doi":"https://doi.org/10.1109/cdc40024.2019.9029363","title":"Linear Encodings for Polytope Containment Problems","display_name":"Linear Encodings for Polytope Containment Problems","publication_year":2019,"publication_date":"2019-12-01","ids":{"openalex":"https://openalex.org/W2922236301","doi":"https://doi.org/10.1109/cdc40024.2019.9029363","mag":"2922236301"},"language":"en","primary_location":{"id":"doi:10.1109/cdc40024.2019.9029363","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9029363","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1903.05214","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034408879","display_name":"Sadra Sadraddini","orcid":"https://orcid.org/0000-0003-2578-8319"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sadra Sadraddini","raw_affiliation_strings":["Computer Science and Artificial Intelligence Laboratory (CSAIL), Massachusetts Institute of Technology, Cambridge, MA","Massachusetts Institute Of Technology#TAB#"],"affiliations":[{"raw_affiliation_string":"Computer Science and Artificial Intelligence Laboratory (CSAIL), Massachusetts Institute of Technology, Cambridge, MA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute Of Technology#TAB#","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074291890","display_name":"Russ Tedrake","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Russ Tedrake","raw_affiliation_strings":["Computer Science and Artificial Intelligence Laboratory (CSAIL), Massachusetts Institute of Technology, Cambridge, MA","Massachusetts Institute Of Technology#TAB#"],"affiliations":[{"raw_affiliation_string":"Computer Science and Artificial Intelligence Laboratory (CSAIL), Massachusetts Institute of Technology, Cambridge, MA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute Of Technology#TAB#","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034408879"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.42838903,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61490612,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"4367","last_page":"4372"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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/T10142","display_name":"Formal Methods in Verification","score":0.9998999834060669,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10933","display_name":"Real-Time Systems Scheduling","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/polytope","display_name":"Polytope","score":0.9283156991004944},{"id":"https://openalex.org/keywords/minkowski-addition","display_name":"Minkowski addition","score":0.7479771375656128},{"id":"https://openalex.org/keywords/polytope-model","display_name":"Polytope model","score":0.7124655246734619},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6836593747138977},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6520205140113831},{"id":"https://openalex.org/keywords/polyhedral-combinatorics","display_name":"Polyhedral combinatorics","score":0.6506072878837585},{"id":"https://openalex.org/keywords/convex-polytope","display_name":"Convex polytope","score":0.5936594009399414},{"id":"https://openalex.org/keywords/birkhoff-polytope","display_name":"Birkhoff polytope","score":0.5802770256996155},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.5733805298805237},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.46605122089385986},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.4657479226589203},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.39976564049720764},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3266980051994324},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.2271224558353424},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2217159867286682},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06860178709030151}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9283156991004944},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.7479771375656128},{"id":"https://openalex.org/C113391598","wikidata":"https://www.wikidata.org/wiki/Q1681391","display_name":"Polytope model","level":3,"score":0.7124655246734619},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6836593747138977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6520205140113831},{"id":"https://openalex.org/C174248988","wikidata":"https://www.wikidata.org/wiki/Q8348314","display_name":"Polyhedral combinatorics","level":5,"score":0.6506072878837585},{"id":"https://openalex.org/C110943637","wikidata":"https://www.wikidata.org/wiki/Q4129097","display_name":"Convex polytope","level":5,"score":0.5936594009399414},{"id":"https://openalex.org/C206304794","wikidata":"https://www.wikidata.org/wiki/Q4916482","display_name":"Birkhoff polytope","level":5,"score":0.5802770256996155},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.5733805298805237},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.46605122089385986},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.4657479226589203},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.39976564049720764},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3266980051994324},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.2271224558353424},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2217159867286682},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06860178709030151},{"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":5,"locations":[{"id":"doi:10.1109/cdc40024.2019.9029363","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc40024.2019.9029363","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 IEEE 58th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1903.05214","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.05214","pdf_url":"https://arxiv.org/pdf/1903.05214","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":"","raw_type":"text"},{"id":"mag:2922236301","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1903.05214","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:dspace.mit.edu:1721.1/137630.2","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/137630.2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"MIT web domain","raw_type":"http://purl.org/eprint/type/ConferencePaper"},{"id":"doi:10.48550/arxiv.1903.05214","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.05214","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1903.05214","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.05214","pdf_url":"https://arxiv.org/pdf/1903.05214","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":"","raw_type":"text"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7099999785423279}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2922236301.pdf","grobid_xml":"https://content.openalex.org/works/W2922236301.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W53671252","https://openalex.org/W1495119384","https://openalex.org/W1545324631","https://openalex.org/W1569692898","https://openalex.org/W1709870800","https://openalex.org/W1968718177","https://openalex.org/W1970227471","https://openalex.org/W1977985274","https://openalex.org/W1978492002","https://openalex.org/W1983281982","https://openalex.org/W1987592584","https://openalex.org/W1998137637","https://openalex.org/W2000147742","https://openalex.org/W2037690395","https://openalex.org/W2057553555","https://openalex.org/W2071775092","https://openalex.org/W2100538121","https://openalex.org/W2116403087","https://openalex.org/W2117535703","https://openalex.org/W2129894900","https://openalex.org/W2160754664","https://openalex.org/W2166156256","https://openalex.org/W2228135619","https://openalex.org/W2229008027","https://openalex.org/W2286777929","https://openalex.org/W2529152906","https://openalex.org/W2783032942","https://openalex.org/W2783859738","https://openalex.org/W2808841883","https://openalex.org/W2940189798","https://openalex.org/W2962695108","https://openalex.org/W2967515279","https://openalex.org/W3106144869","https://openalex.org/W4234356172","https://openalex.org/W6659971213","https://openalex.org/W6679047006","https://openalex.org/W6684351881","https://openalex.org/W6689527168","https://openalex.org/W6696090594"],"related_works":["https://openalex.org/W3012067785","https://openalex.org/W2017624835","https://openalex.org/W2464153233","https://openalex.org/W2963299397","https://openalex.org/W2039080713","https://openalex.org/W2077831283","https://openalex.org/W3046243501","https://openalex.org/W29206020","https://openalex.org/W2517156282","https://openalex.org/W2400973221","https://openalex.org/W3128934906","https://openalex.org/W2057480025","https://openalex.org/W2045645047","https://openalex.org/W69628221","https://openalex.org/W2072503362","https://openalex.org/W760225490","https://openalex.org/W1678771453","https://openalex.org/W2014054476","https://openalex.org/W2894338559","https://openalex.org/W2335963636"],"abstract_inverted_index":{"The":[0,34],"polytope":[1,8],"containment":[2,184],"problem":[3,16,121],"is":[4,9,17,50,106,123],"deciding":[5],"whether":[6],"a":[7,10,51,116,126,174],"contained":[11],"within":[12],"another":[13],"polytope.":[14,141],"This":[15],"rooted":[18],"in":[19,24,97,104],"computational":[20],"convexity,":[21],"and":[22,29,74,92,150,170,197,208],"arises":[23],"applications":[25,56],"such":[26],"as":[27,67,85,125,167],"verification":[28,207],"control":[30],"of":[31,61,72,78,102,137,139,152,165,194,201],"dynamical":[32],"systems.":[33,212],"complexity":[35],"heavily":[36],"depends":[37],"on":[38,144,181,204],"how":[39],"the":[40,100,135,182,199],"polytopes":[41,45,166],"are":[42,154],"represented.":[43],"Describing":[44],"by":[46],"their":[47],"hyperplanes":[48,138],"(H-polytopes)":[49],"popular":[52],"representation.":[53],"In":[54,111],"many":[55],"we":[57,64,114],"use":[58],"affine":[59],"transformations":[60],"H-polytopes,":[62,73],"which":[63],"refer":[65],"to":[66,108,161],"AH-polytopes.":[68,86],"Zonotopes,":[69],"orthogonal":[70,195],"projections":[71],"convex":[75,148,175],"hulls/Minkowski":[76],"sums":[77],"multiple":[79],"H-polytopes":[80,153],"can":[81],"be":[82,109],"efficiently":[83],"represented":[84],"While":[87],"there":[88],"exists":[89],"efficient":[90,157],"necessary":[91],"sufficient":[93,117],"conditions":[94],"for":[95,119,210],"AH-polytope":[96,103,105],"H-polytope":[98],"containment,":[99],"case":[101],"known":[107],"NP-complete.":[110],"this":[112,120],"paper,":[113],"provide":[115],"condition":[118],"that":[122,131],"cast":[124],"linear":[127],"program":[128],"with":[129,134],"size":[130],"grows":[132],"linearly":[133],"number":[136],"each":[140],"Special":[142],"cases":[143],"zonotopes,":[145],"Minkowski":[146],"sums,":[147],"hulls,":[149],"disjunctions":[151],"studied.":[155],"These":[156],"encodings":[158],"enable":[159],"us":[160],"designate":[162],"certain":[163],"components":[164],"decision":[168],"variables,":[169],"incorporate":[171],"them":[172],"into":[173],"optimization":[176],"problem.":[177],"We":[178],"present":[179],"examples":[180],"zonotope":[183,189],"problem,":[185],"polytopic":[186],"Hausdorff":[187],"distances,":[188],"order":[190],"reduction,":[191],"inner":[192],"approximations":[193],"projections,":[196],"demonstrate":[198],"usefulness":[200],"our":[202],"results":[203],"formal":[205],"controller":[206],"synthesis":[209],"hybrid":[211]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}