{"id":"https://openalex.org/W29325442","doi":"https://doi.org/10.1080/03155986.2018.1559428","title":"A regularized interior-point method for constrained linear least squares","display_name":"A regularized interior-point method for constrained linear least squares","publication_year":2019,"publication_date":"2019-02-19","ids":{"openalex":"https://openalex.org/W29325442","doi":"https://doi.org/10.1080/03155986.2018.1559428","mag":"29325442"},"language":"en","primary_location":{"id":"doi:10.1080/03155986.2018.1559428","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03155986.2018.1559428","pdf_url":null,"source":{"id":"https://openalex.org/S155959304","display_name":"INFOR Information Systems and Operational Research","issn_l":"0315-5986","issn":["0315-5986","1916-0615"],"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":"INFOR: Information Systems and Operational Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.13140/rg.2.2.18542.51523","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083091154","display_name":"Mohsen Dehghani","orcid":null},"institutions":[{"id":"https://openalex.org/I45683168","display_name":"Polytechnique Montr\u00e9al","ror":"https://ror.org/05f8d4e86","country_code":"CA","type":"education","lineage":["https://openalex.org/I45683168"]},{"id":"https://openalex.org/I4210133247","display_name":"Group for Research in Decision Analysis","ror":"https://ror.org/02pkvpx84","country_code":"CA","type":"facility","lineage":["https://openalex.org/I108192572","https://openalex.org/I159129438","https://openalex.org/I4210133247","https://openalex.org/I45683168","https://openalex.org/I49663120","https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Mohsen Dehghani","raw_affiliation_strings":["GERAD and Department of Mathematics and Industrial Engineering, \u00c9cole Polytechnique de Montr\u00e9al, Montreal, Canada"],"affiliations":[{"raw_affiliation_string":"GERAD and Department of Mathematics and Industrial Engineering, \u00c9cole Polytechnique de Montr\u00e9al, Montreal, Canada","institution_ids":["https://openalex.org/I45683168","https://openalex.org/I4210133247"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090989168","display_name":"Andrew B. Lambe","orcid":"https://orcid.org/0000-0003-1817-4271"},"institutions":[{"id":"https://openalex.org/I45683168","display_name":"Polytechnique Montr\u00e9al","ror":"https://ror.org/05f8d4e86","country_code":"CA","type":"education","lineage":["https://openalex.org/I45683168"]},{"id":"https://openalex.org/I4210133247","display_name":"Group for Research in Decision Analysis","ror":"https://ror.org/02pkvpx84","country_code":"CA","type":"facility","lineage":["https://openalex.org/I108192572","https://openalex.org/I159129438","https://openalex.org/I4210133247","https://openalex.org/I45683168","https://openalex.org/I49663120","https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Andrew Lambe","raw_affiliation_strings":["GERAD and Department of Mathematics and Industrial Engineering, \u00c9cole Polytechnique de Montr\u00e9al, Montreal, Canada"],"affiliations":[{"raw_affiliation_string":"GERAD and Department of Mathematics and Industrial Engineering, \u00c9cole Polytechnique de Montr\u00e9al, Montreal, Canada","institution_ids":["https://openalex.org/I45683168","https://openalex.org/I4210133247"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027758717","display_name":"Dominique Orban","orcid":"https://orcid.org/0000-0002-8017-7687"},"institutions":[{"id":"https://openalex.org/I4210133247","display_name":"Group for Research in Decision Analysis","ror":"https://ror.org/02pkvpx84","country_code":"CA","type":"facility","lineage":["https://openalex.org/I108192572","https://openalex.org/I159129438","https://openalex.org/I4210133247","https://openalex.org/I45683168","https://openalex.org/I49663120","https://openalex.org/I5023651"]},{"id":"https://openalex.org/I45683168","display_name":"Polytechnique Montr\u00e9al","ror":"https://ror.org/05f8d4e86","country_code":"CA","type":"education","lineage":["https://openalex.org/I45683168"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Dominique Orban","raw_affiliation_strings":["GERAD and Department of Mathematics and Industrial Engineering, \u00c9cole Polytechnique de Montr\u00e9al, Montreal, Canada"],"affiliations":[{"raw_affiliation_string":"GERAD and Department of Mathematics and Industrial Engineering, \u00c9cole Polytechnique de Montr\u00e9al, Montreal, Canada","institution_ids":["https://openalex.org/I45683168","https://openalex.org/I4210133247"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090989168"],"corresponding_institution_ids":["https://openalex.org/I4210133247","https://openalex.org/I45683168"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"58","issue":"2","first_page":"202","last_page":"224"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9970999956130981,"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":0.9970999956130981,"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":0.9962000250816345,"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":0.9865000247955322,"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/mathematics","display_name":"Mathematics","score":0.7043343186378479},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.5058164596557617},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4842824339866638},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.47137367725372314},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.44890090823173523},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4320030212402344},{"id":"https://openalex.org/keywords/positive-definite-matrix","display_name":"Positive-definite matrix","score":0.4249560832977295},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4217146039009094},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.414320170879364},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38412874937057495},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34054237604141235},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3347911834716797},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3229120373725891},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21447762846946716},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.13734915852546692},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12961944937705994},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1145118772983551}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7043343186378479},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.5058164596557617},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4842824339866638},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.47137367725372314},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.44890090823173523},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4320030212402344},{"id":"https://openalex.org/C49712288","wikidata":"https://www.wikidata.org/wiki/Q77601250","display_name":"Positive-definite matrix","level":3,"score":0.4249560832977295},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4217146039009094},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.414320170879364},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38412874937057495},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34054237604141235},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3347911834716797},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3229120373725891},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21447762846946716},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.13734915852546692},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12961944937705994},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1145118772983551},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1080/03155986.2018.1559428","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03155986.2018.1559428","pdf_url":null,"source":{"id":"https://openalex.org/S155959304","display_name":"INFOR Information Systems and Operational Research","issn_l":"0315-5986","issn":["0315-5986","1916-0615"],"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":"INFOR: Information Systems and Operational Research","raw_type":"journal-article"},{"id":"mag:29325442","is_oa":false,"landing_page_url":"https://www.gerad.ca/en/papers/G-2018-07","pdf_url":null,"source":{"id":"https://openalex.org/S4306518497","display_name":"Les Cahiers du GERAD","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Les Cahiers du GERAD","raw_type":null},{"id":"pmh:oai:publications.polymtl.ca:1121","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"NonPeerReviewed"},{"id":"pmh:oai:publications.polymtl.ca:43143","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/43143/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"},{"id":"doi:10.13140/rg.2.2.18542.51523","is_oa":true,"landing_page_url":"https://doi.org/10.13140/rg.2.2.18542.51523","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.13140/rg.2.2.18542.51523","is_oa":true,"landing_page_url":"https://doi.org/10.13140/rg.2.2.18542.51523","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7417830218","display_name":null,"funder_award_id":"10-04","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"}],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1967810262","https://openalex.org/W1986858853","https://openalex.org/W1986931325","https://openalex.org/W2009926490","https://openalex.org/W2010237532","https://openalex.org/W2033477411","https://openalex.org/W2033624514","https://openalex.org/W2050834445","https://openalex.org/W2056950638","https://openalex.org/W2060778176","https://openalex.org/W2069159962","https://openalex.org/W2075665712","https://openalex.org/W2075998338","https://openalex.org/W2076605490","https://openalex.org/W2082290366","https://openalex.org/W2086867325","https://openalex.org/W2118341515","https://openalex.org/W2135779729","https://openalex.org/W2169743588","https://openalex.org/W2609118327","https://openalex.org/W3022380717","https://openalex.org/W4245456352","https://openalex.org/W4254106911","https://openalex.org/W4302564868"],"related_works":["https://openalex.org/W1539312801","https://openalex.org/W2089312400","https://openalex.org/W2964074410","https://openalex.org/W1545452030","https://openalex.org/W2339289811","https://openalex.org/W2159193939","https://openalex.org/W2010737672","https://openalex.org/W1744745307","https://openalex.org/W2143216521","https://openalex.org/W996738808","https://openalex.org/W2936066494","https://openalex.org/W1994870183","https://openalex.org/W2962823551","https://openalex.org/W3100222695","https://openalex.org/W1549932963","https://openalex.org/W2527075805","https://openalex.org/W2953122368","https://openalex.org/W2048880346","https://openalex.org/W2963402842","https://openalex.org/W2889890251"],"abstract_inverted_index":{"We":[0,106,121],"propose":[1],"an":[2],"infeasible":[3],"interior-point":[4],"algorithm":[5],"for":[6],"constrained":[7,116],"linear":[8,42,64,90,94,100],"least-squares":[9,95,117],"problems":[10,96],"based":[11],"on":[12,85],"the":[13,29,32,63,86,99,114,126,132],"primal-dual":[14],"regularization":[15],"of":[16,19,113,135],"convex":[17],"programs":[18],"Friedlander":[20],"and":[21,60,92,130],"Orban.":[22],"Regularization":[23],"allows":[24],"us":[25],"to":[26,56,97],"dispense":[27],"with":[28,44,102,125],"assumption":[30],"that":[31,75],"active":[33],"gradients":[34],"are":[35],"linearly":[36],"independent.":[37],"At":[38],"each":[39],"iteration,":[40],"a":[41,45,111],"system":[43,65,101],"symmetric":[46],"quasi-definite":[47],"(SQD)":[48],"matrix":[49,53],"is":[50,54,119],"solved.":[51],"This":[52],"shown":[55],"be":[57,67,79],"uniformly":[58],"bounded":[59],"nonsingular.":[61],"While":[62],"may":[66,78],"solved":[68],"using":[69],"sparse":[70,103,127],"LDLT":[71],"factorization,":[72],"we":[73,83],"observe":[74],"other":[76],"approaches":[77],"used.":[80],"In":[81],"particular,":[82],"build":[84],"connection":[87],"between":[88],"SQD":[89],"systems":[91],"unconstrained":[93],"solve":[98],"QR":[104,128],"factorization.":[105],"establish":[107],"conditions":[108],"under":[109],"which":[110],"solution":[112],"original,":[115],"problem":[118],"recovered.":[120],"report":[122],"computational":[123],"experience":[124],"factorization":[129],"illustrate":[131],"potential":[133],"advantages":[134],"our":[136],"approach.":[137]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}