{"id":"https://openalex.org/W2791001823","doi":"https://doi.org/10.1080/10556788.2019.1615910","title":"Computational performance of a projection and rescaling algorithm","display_name":"Computational performance of a projection and rescaling algorithm","publication_year":2019,"publication_date":"2019-05-16","ids":{"openalex":"https://openalex.org/W2791001823","doi":"https://doi.org/10.1080/10556788.2019.1615910","mag":"2791001823"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2019.1615910","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2019.1615910","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1803.07107","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016340912","display_name":"Javier Pe\u00f1a","orcid":"https://orcid.org/0000-0001-5698-1918"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Javier Pe\u00f1a","raw_affiliation_strings":["Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA","Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020328383","display_name":"Negar Soheili","orcid":"https://orcid.org/0000-0002-2114-5319"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Negar Soheili","raw_affiliation_strings":["College of Business Administration, University of Illinois at Chicago, Chicago, IL, USA","University of Illinois at #TAB#Chicago"],"affiliations":[{"raw_affiliation_string":"College of Business Administration, University of Illinois at Chicago, Chicago, IL, USA","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"University of Illinois at #TAB#Chicago","institution_ids":["https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5016340912"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00694123,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"36","issue":"5","first_page":"934","last_page":"951"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983000159263611,"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":0.9983000159263611,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9861000180244446,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9660999774932861,"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/projection","display_name":"Projection (relational algebra)","score":0.7538784742355347},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.7204056978225708},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.7178322076797485},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.7153877019882202},{"id":"https://openalex.org/keywords/matlab","display_name":"MATLAB","score":0.7044481039047241},{"id":"https://openalex.org/keywords/orthogonal-complement","display_name":"Orthogonal complement","score":0.6638056039810181},{"id":"https://openalex.org/keywords/orthographic-projection","display_name":"Orthographic projection","score":0.5638379454612732},{"id":"https://openalex.org/keywords/simplicity","display_name":"Simplicity","score":0.5503673553466797},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49743393063545227},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4952322542667389},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.4420279264450073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.38229164481163025},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3231552243232727},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14880570769309998},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11187967658042908}],"concepts":[{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.7538784742355347},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7204056978225708},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.7178322076797485},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.7153877019882202},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.7044481039047241},{"id":"https://openalex.org/C154399039","wikidata":"https://www.wikidata.org/wiki/Q1780921","display_name":"Orthogonal complement","level":3,"score":0.6638056039810181},{"id":"https://openalex.org/C175694140","wikidata":"https://www.wikidata.org/wiki/Q980329","display_name":"Orthographic projection","level":2,"score":0.5638379454612732},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.5503673553466797},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49743393063545227},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4952322542667389},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4420279264450073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38229164481163025},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3231552243232727},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14880570769309998},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11187967658042908},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10556788.2019.1615910","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2019.1615910","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"},{"id":"pmh:oai:arXiv.org:1803.07107","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.07107","pdf_url":"https://arxiv.org/pdf/1803.07107","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:2791001823","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1803.07107.pdf","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":"doi:10.48550/arxiv.1803.07107","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.07107","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:1803.07107","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.07107","pdf_url":"https://arxiv.org/pdf/1803.07107","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":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2791001823.pdf","grobid_xml":"https://content.openalex.org/works/W2791001823.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1572529050","https://openalex.org/W1605451826","https://openalex.org/W2009932696","https://openalex.org/W2020361255","https://openalex.org/W2040392433","https://openalex.org/W2100793163","https://openalex.org/W2146738285","https://openalex.org/W2491133435","https://openalex.org/W2551627961","https://openalex.org/W2567550261","https://openalex.org/W2570866188","https://openalex.org/W2612034470","https://openalex.org/W2754872025","https://openalex.org/W2780582866","https://openalex.org/W2964186244","https://openalex.org/W3098696827"],"related_works":["https://openalex.org/W2981839384","https://openalex.org/W2047092297","https://openalex.org/W3158421934","https://openalex.org/W2899649398","https://openalex.org/W3102206315","https://openalex.org/W3082211258","https://openalex.org/W2159915812","https://openalex.org/W2789604698","https://openalex.org/W2187630693","https://openalex.org/W3129191441","https://openalex.org/W1989275682","https://openalex.org/W2889429527","https://openalex.org/W3038015759","https://openalex.org/W3030121914","https://openalex.org/W3181157392","https://openalex.org/W3120036018","https://openalex.org/W2508866287","https://openalex.org/W3095955021","https://openalex.org/W2963188969","https://openalex.org/W3133264924"],"abstract_inverted_index":{"This":[0],"paper":[1],"documents":[2],"a":[3,7,29,46,52,60,66,70,120],"computational":[4,93,121],"implementation":[5,72,122],"of":[6,20,69,73,80,90,98,101,116],"projection":[8,41,103],"and":[9,34,42,76,104],"rescaling":[10,43,62,105],"algorithm":[11,44,75,118],"for":[12],"finding":[13],"most":[14],"interior":[15],"solutions":[16],"to":[17],"the":[18,99,102,114,117],"pair":[19],"feasibility":[21],"problems":[22],"find":[23],"x\u2208L\u2229R+nandfind":[24],"x\u02c6\u2208L\u22a5\u2229R+n,":[25],"where":[26],"L":[27],"denotes":[28,36],"linear":[30],"subspace":[31],"in":[32,123],"Rn":[33],"L\u22a5":[35],"its":[37],"orthogonal":[38],"complement.":[39],"The":[40],"is":[45,110],"recently":[47],"developed":[48],"method":[49],"that":[50],"combines":[51],"basic":[53],"procedure":[54],"involving":[55],"only":[56],"low-cost":[57],"operations":[58],"with":[59,87],"periodic":[61],"step.":[63],"We":[64],"give":[65],"full":[67],"description":[68],"MATLAB":[71,108],"this":[74],"present":[77],"multiple":[78],"sets":[79],"numerical":[81],"experiments":[82,94],"on":[83],"synthetic":[84],"problem":[85],"instances":[86],"varied":[88],"levels":[89],"conditioning.":[91],"Our":[92,107],"provide":[95],"promising":[96],"evidence":[97],"effectiveness":[100],"algorithm.":[106],"code":[109],"publicly":[111],"available.":[112],"Furthermore,":[113],"simplicity":[115],"makes":[119],"other":[124],"environments":[125],"completely":[126],"straightforward.":[127]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}