{"id":"https://openalex.org/W3008048690","doi":"https://doi.org/10.1137/20m1324417","title":"Lifting for Simplicity: Concise Descriptions of Convex Sets","display_name":"Lifting for Simplicity: Concise Descriptions of Convex Sets","publication_year":2022,"publication_date":"2022-11-01","ids":{"openalex":"https://openalex.org/W3008048690","doi":"https://doi.org/10.1137/20m1324417","mag":"3008048690"},"language":"en","primary_location":{"id":"doi:10.1137/20m1324417","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1324417","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2002.09788","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017261970","display_name":"Hamza Fawzi","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]},{"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"]},{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["AU","GB","PT","US"],"is_corresponding":false,"raw_author_name":"Hamza Fawzi","raw_affiliation_strings":["Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA","Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, United Kingdom","Department of Electrical and Computer Systems Engineering, Monash University, VIC 3800, Aus-tralia","Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA","CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal"],"raw_orcid":"https://orcid.org/0000-0001-6026-4102","affiliations":[{"raw_affiliation_string":"Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, United Kingdom","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Department of Electrical and Computer Systems Engineering, Monash University, VIC 3800, Aus-tralia","institution_ids":["https://openalex.org/I56590836"]},{"raw_affiliation_string":"Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017216022","display_name":"Jo\u00e3o Gouveia","orcid":"https://orcid.org/0000-0001-8345-9754"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]},{"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"]},{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["AU","GB","PT","US"],"is_corresponding":false,"raw_author_name":"Joao Gouveia","raw_affiliation_strings":["Department of Electrical and Computer Systems Engineering, Monash University, VIC 3800, Aus-tralia","Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, United Kingdom","Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA","CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal","Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA"],"raw_orcid":"https://orcid.org/0000-0001-8345-9754","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Systems Engineering, Monash University, VIC 3800, Aus-tralia","institution_ids":["https://openalex.org/I56590836"]},{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, United Kingdom","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]},{"raw_affiliation_string":"Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031935416","display_name":"Pablo A. Parrilo","orcid":"https://orcid.org/0000-0003-1132-8477"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]},{"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"]},{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["AU","GB","PT","US"],"is_corresponding":false,"raw_author_name":"Pablo A. Parrilo","raw_affiliation_strings":["Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, United Kingdom","Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA","CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal","Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA","Department of Electrical and Computer Systems Engineering, Monash University, VIC 3800, Aus-tralia"],"raw_orcid":"https://orcid.org/0000-0003-1132-8477","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, United Kingdom","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]},{"raw_affiliation_string":"Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Electrical and Computer Systems Engineering, Monash University, VIC 3800, Aus-tralia","institution_ids":["https://openalex.org/I56590836"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037774037","display_name":"James Saunderson","orcid":"https://orcid.org/0000-0002-5456-0180"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]},{"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"]},{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["AU","GB","PT","US"],"is_corresponding":false,"raw_author_name":"James Saunderson","raw_affiliation_strings":["Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA","Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA","Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, United Kingdom","CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal","Department of Electrical and Computer Systems Engineering, Monash University, VIC 3800, Aus-tralia"],"raw_orcid":"https://orcid.org/0000-0002-5456-0180","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA","institution_ids":["https://openalex.org/I201448701"]},{"raw_affiliation_string":"Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, United Kingdom","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]},{"raw_affiliation_string":"Department of Electrical and Computer Systems Engineering, Monash University, VIC 3800, Aus-tralia","institution_ids":["https://openalex.org/I56590836"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047323505","display_name":"Rekha R. Thomas","orcid":"https://orcid.org/0000-0003-2189-2303"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]},{"id":"https://openalex.org/I4210143601","display_name":"Decision Systems (United States)","ror":"https://ror.org/0434dpa13","country_code":"US","type":"company","lineage":["https://openalex.org/I4210143601"]},{"id":"https://openalex.org/I56590836","display_name":"Monash University","ror":"https://ror.org/02bfwt286","country_code":"AU","type":"education","lineage":["https://openalex.org/I56590836"]},{"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"]},{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["AU","GB","PT","US"],"is_corresponding":false,"raw_author_name":"Rekha R. Thomas","raw_affiliation_strings":["Department of Electrical and Computer Systems Engineering, Monash University, VIC 3800, Aus-tralia","Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, United Kingdom","CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal","Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA","Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Systems Engineering, Monash University, VIC 3800, Aus-tralia","institution_ids":["https://openalex.org/I56590836"]},{"raw_affiliation_string":"Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 0WA, United Kingdom","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]},{"raw_affiliation_string":"Laboratory for Information and Decision Systems (LIDS), Massachusetts Institute of Technology, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I4210143601","https://openalex.org/I63966007"]},{"raw_affiliation_string":"Department of Mathematics, University of Washington, Box 354350, Seattle, WA 98195, USA","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.217,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.80526969,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"64","issue":"4","first_page":"866","last_page":"918"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9915000200271606,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9915000200271606,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9911999702453613,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9861000180244446,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6902231574058533},{"id":"https://openalex.org/keywords/lift","display_name":"Lift (data mining)","score":0.6890369653701782},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.5770294666290283},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5316451191902161},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4943842887878418},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.46828290820121765},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4657823443412781},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.4496217966079712},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4318258762359619},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.42960861325263977},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.4147634208202362},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3406968116760254},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3255004286766052},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2876847982406616},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10720184445381165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6902231574058533},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.6890369653701782},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.5770294666290283},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5316451191902161},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4943842887878418},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.46828290820121765},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4657823443412781},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.4496217966079712},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4318258762359619},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.42960861325263977},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.4147634208202362},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3406968116760254},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3255004286766052},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2876847982406616},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10720184445381165},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/20m1324417","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1324417","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2002.09788","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.09788","pdf_url":"https://arxiv.org/pdf/2002.09788","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:dspace.mit.edu:1721.1/165366","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/165366","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","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Society for Industrial & Applied Mathematics (SIAM)","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2002.09788","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2002.09788","pdf_url":"https://arxiv.org/pdf/2002.09788","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":[{"id":"https://openalex.org/G1617160020","display_name":null,"funder_award_id":"CCF-1565235","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4941397794","display_name":null,"funder_award_id":"UIDB/00324/2020","funder_id":"https://openalex.org/F4320323392","funder_display_name":"Universidade de Coimbra"},{"id":"https://openalex.org/G6101260676","display_name":null,"funder_award_id":"DE210101056","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G6700137421","display_name":null,"funder_award_id":"DMS-1719538","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320323392","display_name":"Universidade de Coimbra","ror":"https://ror.org/04z8k9a98"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":104,"referenced_works":["https://openalex.org/W32980360","https://openalex.org/W143396352","https://openalex.org/W144954708","https://openalex.org/W608042232","https://openalex.org/W1507415131","https://openalex.org/W1528304975","https://openalex.org/W1534511674","https://openalex.org/W1563391815","https://openalex.org/W1568307856","https://openalex.org/W1632601927","https://openalex.org/W1652518220","https://openalex.org/W1658982721","https://openalex.org/W1664429083","https://openalex.org/W1755753347","https://openalex.org/W1840847274","https://openalex.org/W1945057103","https://openalex.org/W1965650902","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1968321268","https://openalex.org/W1968936725","https://openalex.org/W1974962384","https://openalex.org/W1975335740","https://openalex.org/W1979423085","https://openalex.org/W1985123706","https://openalex.org/W1985215886","https://openalex.org/W1986105362","https://openalex.org/W1987569845","https://openalex.org/W1991813962","https://openalex.org/W2012937096","https://openalex.org/W2019669853","https://openalex.org/W2024063662","https://openalex.org/W2024340911","https://openalex.org/W2028777326","https://openalex.org/W2031923588","https://openalex.org/W2049143039","https://openalex.org/W2061987651","https://openalex.org/W2068066892","https://openalex.org/W2071242430","https://openalex.org/W2073576149","https://openalex.org/W2077397558","https://openalex.org/W2078600458","https://openalex.org/W2079135578","https://openalex.org/W2080267935","https://openalex.org/W2082242399","https://openalex.org/W2089457275","https://openalex.org/W2098329933","https://openalex.org/W2100440346","https://openalex.org/W2106264302","https://openalex.org/W2107395148","https://openalex.org/W2120092158","https://openalex.org/W2123640521","https://openalex.org/W2124172487","https://openalex.org/W2126138717","https://openalex.org/W2126210866","https://openalex.org/W2128536529","https://openalex.org/W2138677859","https://openalex.org/W2152557171","https://openalex.org/W2153400929","https://openalex.org/W2160467746","https://openalex.org/W2163803752","https://openalex.org/W2163916252","https://openalex.org/W2165281529","https://openalex.org/W2168881618","https://openalex.org/W2171048418","https://openalex.org/W2239251014","https://openalex.org/W2255400221","https://openalex.org/W2266668300","https://openalex.org/W2321429733","https://openalex.org/W2337855014","https://openalex.org/W2345805953","https://openalex.org/W2487893106","https://openalex.org/W2493312408","https://openalex.org/W2536897863","https://openalex.org/W2557774354","https://openalex.org/W2620334136","https://openalex.org/W2744182242","https://openalex.org/W2752158681","https://openalex.org/W2759253428","https://openalex.org/W2912522929","https://openalex.org/W2948186597","https://openalex.org/W2950206471","https://openalex.org/W2954040150","https://openalex.org/W2962902171","https://openalex.org/W2963010019","https://openalex.org/W2963878374","https://openalex.org/W2963948022","https://openalex.org/W2964325641","https://openalex.org/W2973187509","https://openalex.org/W2988480584","https://openalex.org/W3014980195","https://openalex.org/W3037265734","https://openalex.org/W3037753594","https://openalex.org/W3099415239","https://openalex.org/W3099419577","https://openalex.org/W3103158853","https://openalex.org/W3105023213","https://openalex.org/W3105624319","https://openalex.org/W3123950972","https://openalex.org/W3187545495","https://openalex.org/W4249667877","https://openalex.org/W4252077841","https://openalex.org/W4256587124","https://openalex.org/W4293860921"],"related_works":["https://openalex.org/W868123585","https://openalex.org/W2391247224","https://openalex.org/W2026600343","https://openalex.org/W2374624997","https://openalex.org/W4311073519","https://openalex.org/W2356261519","https://openalex.org/W4382519084","https://openalex.org/W2478309485","https://openalex.org/W2913596570","https://openalex.org/W2002037426"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,19,23,86,96,106,136,154,225],"selected":[4],"tour":[5],"through":[6],"the":[7,30,45,63,128,131,162,172,187,197,204,217,220,232],"theory":[8],"and":[9,139,170,196,236,247],"applications":[10],"of":[11,13,18,66,77,133,135,143,159,164,167,177,184,189,203,219,227,234,240,245],"lifts":[12,37,51,134,166,235,241],"convex":[14,20,25,34,97,137,168],"sets.":[15],"A":[16],"lift":[17,111,120],"set":[21,26,138,205],"is":[22,121,214],"higher-dimensional":[24],"that":[27,38,76,117],"projects":[28],"onto":[29],"original":[31,46],"set.":[32,47],"Many":[33],"sets":[35,169],"have":[36],"are":[39],"dramatically":[40],"simpler":[41],"to":[42,92,103,161,186,193,200,215,231],"describe":[43,153],"than":[44,209],"Finding":[48],"such":[49,119],"simple":[50],"has":[52],"significant":[53],"algorithmic":[54],"implications,":[55],"particularly":[56],"for":[57],"optimization":[58],"problems.":[59],"We":[60,222],"consider":[61],"both":[62],"classical":[64],"case":[65],"polyhedral":[67,108],"lifts,":[68,79],"described":[69],"by":[70,81],"linear":[71,82],"inequalities,":[72,84],"as":[73,75],"well":[74],"spectrahedral":[78,93,110,165],"defined":[80],"matrix":[83],"with":[85],"focus":[87],"on":[88,149,174,224],"recent":[89],"developments":[90],"related":[91,192,199,230],"lifts.":[94],"Given":[95],"set,":[98],"ideally":[99],"we":[100,126,152,180],"would":[101],"like":[102],"either":[104],"find":[105,113],"(low-complexity)":[107],"or":[109,112],"an":[114],"obstruction":[115,185],"proving":[116],"no":[118],"possible.":[122],"To":[123],"this":[124,150],"end,":[125],"explain":[127],"connection":[129],"between":[130],"existence":[132,188,233],"certain":[140],"structured":[141],"factorizations":[142],"its":[144,248],"associated":[145],"slack":[146],"operator.":[147],"Based":[148],"characterization,":[151],"uniform":[155],"approach,":[156],"via":[157],"sums":[158],"squares,":[160],"construction":[163],"illustrate":[171,216],"method":[173],"several":[175],"families":[176],"examples.":[178],"Finally,":[179],"discuss":[181],"two":[182],"flavors":[183],"lifts:":[190],"one":[191],"facial":[194],"structure,":[195],"other":[198],"algebraic":[201],"properties":[202],"in":[206],"question.":[207],"Rather":[208],"being":[210],"exhaustive,":[211],"our":[212],"aim":[213],"richness":[218],"area.":[221],"touch":[223],"range":[226],"different":[228,243],"topics":[229],"present":[237],"many":[238],"examples":[239],"from":[242],"areas":[244],"mathematics":[246],"applications.":[249]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}