{"id":"https://openalex.org/W2339880967","doi":"https://doi.org/10.68381/jca23016","title":"How the Augmented Lagrangian Algorithm Can Deal with an Infeasible Convex Quadratic Optimization Problem","display_name":"How the Augmented Lagrangian Algorithm Can Deal with an Infeasible Convex Quadratic Optimization Problem","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2339880967","doi":"https://doi.org/10.68381/jca23016","mag":"2339880967"},"language":"en","primary_location":{"id":"doi:10.68381/jca23016","doi":"https://doi.org/10.68381/jca23016","is_oa":true,"landing_page_url":"https://doi.org/10.68381/jca23016","pdf_url":"https://journalofconvexanalysis.com/articles/jca23016/jca23016.pdf","source":{"id":"https://openalex.org/S163398844","display_name":"Journal of convex analysis","issn_l":"0944-6532","issn":["0944-6532","2363-6394"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"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":"Journal of Convex Analysis","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://journalofconvexanalysis.com/articles/jca23016/jca23016.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085077329","display_name":"Alice Chiche","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210108130","display_name":"Artelys (France)","ror":"https://ror.org/01fzeeh76","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210108130"]},{"id":"https://openalex.org/I4210143116","display_name":"\u00c9lectricit\u00e9 de France (France)","ror":"https://ror.org/03wb8xz10","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210143116"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alice Chiche","raw_affiliation_strings":["Artelys France, 12 rue du Quatre Septembre, 75002 Paris, France","EDF R&D, Osiris departement, 1, avenue du G\u00e9n\u00e9ral de Gaulle, 92141 Clamart Cedex, France","INRIA Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France","Optimisation, Simulation, Risque et Statistiques pour les March\u00e9s de l\u2019Energie"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Artelys France, 12 rue du Quatre Septembre, 75002 Paris, France","institution_ids":["https://openalex.org/I4210108130"]},{"raw_affiliation_string":"EDF R&D, Osiris departement, 1, avenue du G\u00e9n\u00e9ral de Gaulle, 92141 Clamart Cedex, France","institution_ids":["https://openalex.org/I4210143116"]},{"raw_affiliation_string":"INRIA Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Optimisation, Simulation, Risque et Statistiques pour les March\u00e9s de l\u2019Energie","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033475682","display_name":"Jean Charles Gilbert","orcid":"https://orcid.org/0000-0002-0375-4663","observed_orcids":["https://orcid.org/0000-0002-0375-4663"]},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean Charles Gilbert","raw_affiliation_strings":["INRIA Paris, 2 Rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France","Environmental Modeling, Optimization and Programming Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INRIA Paris, 2 Rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"Environmental Modeling, Optimization and Programming Models","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1171,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.72396885,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":87,"max":98},"biblio":{"volume":"23","issue":"2","first_page":"425","last_page":"459"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.8701000213623047,"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":0.8701000213623047,"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":0.125,"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":0.0017999999690800905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"augmented Lagrangian method","score":0.9269999861717224},{"id":"https://openalex.org/keywords/global-linear-convergence","display_name":"global linear convergence","score":0.8989999890327454},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.5669999718666077}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.7664667367935181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6331498026847839},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6255274415016174},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5611450672149658},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5395909547805786},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.5188297033309937},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5156470537185669},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5002188682556152},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4992334842681885},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4562987983226776},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4269302487373352},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.42551130056381226},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.4192146062850952},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4147534668445587},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4104253351688385},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3891112208366394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23043420910835266},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.10320881009101868},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.68381/jca23016","doi":"https://doi.org/10.68381/jca23016","is_oa":true,"landing_page_url":"https://doi.org/10.68381/jca23016","pdf_url":"https://journalofconvexanalysis.com/articles/jca23016/jca23016.pdf","source":{"id":"https://openalex.org/S163398844","display_name":"Journal of convex analysis","issn_l":"0944-6532","issn":["0944-6532","2363-6394"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"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":"Journal of Convex Analysis","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01057577v1","doi":null,"is_oa":true,"landing_page_url":"https://inria.hal.science/hal-01057577","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.heldermann.de/JCA/JCA23/JCA232/jca23016.htm","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-01111126v1","doi":null,"is_oa":false,"landing_page_url":"https://hal.inria.fr/hal-01111126","pdf_url":null,"source":{"id":"https://openalex.org/S4377196329","display_name":"HAL Portal Artxiker (Hindustan Aeronautics Limited (India))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4210088939","host_organization_name":"Hindustan Aeronautics Limited (India)","host_organization_lineage":["https://openalex.org/I4210088939"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Convex Analysis","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.68381/jca23016","doi":"https://doi.org/10.68381/jca23016","is_oa":true,"landing_page_url":"https://doi.org/10.68381/jca23016","pdf_url":"https://journalofconvexanalysis.com/articles/jca23016/jca23016.pdf","source":{"id":"https://openalex.org/S163398844","display_name":"Journal of convex analysis","issn_l":"0944-6532","issn":["0944-6532","2363-6394"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"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":"Journal of Convex Analysis","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321663","display_name":"Association Nationale de la Recherche et de la Technologie","ror":"https://ror.org/00ht2ab73"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2339880967.pdf","grobid_xml":"https://content.openalex.org/works/W2339880967.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W2572016","https://openalex.org/W19898668","https://openalex.org/W35651078","https://openalex.org/W80289139","https://openalex.org/W111413457","https://openalex.org/W147998453","https://openalex.org/W182881619","https://openalex.org/W257907672","https://openalex.org/W388179047","https://openalex.org/W631291837","https://openalex.org/W646582900","https://openalex.org/W1499439642","https://openalex.org/W1552557896","https://openalex.org/W1577338488","https://openalex.org/W1885585144","https://openalex.org/W1953936588","https://openalex.org/W1970101292","https://openalex.org/W1982165727","https://openalex.org/W1989033306","https://openalex.org/W1998260066","https://openalex.org/W2005865517","https://openalex.org/W2027347504","https://openalex.org/W2033736734","https://openalex.org/W2033758151","https://openalex.org/W2037091587","https://openalex.org/W2038497950","https://openalex.org/W2038904236","https://openalex.org/W2042532613","https://openalex.org/W2046866204","https://openalex.org/W2052312775","https://openalex.org/W2052782332","https://openalex.org/W2056868378","https://openalex.org/W2057624533","https://openalex.org/W2058021091","https://openalex.org/W2062320580","https://openalex.org/W2071213012","https://openalex.org/W2071402680","https://openalex.org/W2071410137","https://openalex.org/W2083432309","https://openalex.org/W2084478514","https://openalex.org/W2090589861","https://openalex.org/W2091371007","https://openalex.org/W2107465205","https://openalex.org/W2110018596","https://openalex.org/W2136885855","https://openalex.org/W2138216979","https://openalex.org/W2142333440","https://openalex.org/W2157570139","https://openalex.org/W2164224215","https://openalex.org/W2185133926","https://openalex.org/W2198183204","https://openalex.org/W3012080241","https://openalex.org/W4249513058","https://openalex.org/W4253214256","https://openalex.org/W4293820388","https://openalex.org/W4301283118","https://openalex.org/W4302155765","https://openalex.org/W7095226123"],"related_works":["https://openalex.org/W2422409469","https://openalex.org/W2892650854","https://openalex.org/W2096686957","https://openalex.org/W1967695340","https://openalex.org/W1966781202","https://openalex.org/W1982935349","https://openalex.org/W4416261766","https://openalex.org/W2051311328","https://openalex.org/W2198183204","https://openalex.org/W7095226123"],"abstract_inverted_index":{"This":[0,83],"paper":[1],"analyses":[2],"the":[3,6,24,31,35,39,49,53,56,80,90,97,102,111,120],"behavior":[4],"of":[5,63,99,101,113],"augmented":[7],"Lagrangian":[8],"algorithm":[9,25],"when":[10,119],"it":[11],"deals":[12],"with":[13,72],"an":[14],"infeasible":[15],"convex":[16],"quadratic":[17],"optimization":[18],"problem.":[19],"It":[20],"is":[21,69,76,122],"shown":[22],"that":[23,43,75,93],"finds":[26],"a":[27,67,73,86],"point":[28,68],"that,":[29],"on":[30,48,55],"one":[32],"hand,":[33,51],"satisfies":[34],"constraints":[36],"shifted":[37,58,103],"by":[38],"smallest":[40],"possible":[41],"shift":[42],"makes":[44],"them":[45],"feasible":[46],"and,":[47],"other":[50],"minimizes":[52],"objective":[54],"corresponding":[57],"constrained":[59],"set.":[60],"The":[61],"speed":[62,98],"convergence":[64,100],"to":[65,79,106],"such":[66],"globally":[70],"linear,":[71],"rate":[74],"inversely":[77],"proportional":[78],"augmentation":[81,91,116],"parameter.":[82],"suggests":[84],"us":[85],"rule":[87,109],"for":[88],"determining":[89],"parameter":[92],"aims":[94],"at":[95],"controlling":[96],"constraint":[104],"norm":[105],"zero;":[107],"this":[108],"has":[110],"advantage":[112],"generating":[114],"bounded":[115],"parameters":[117],"even":[118],"problem":[121],"infeasible.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2016-06-24T00:00:00"}
