{"id":"https://openalex.org/W1977244564","doi":"https://doi.org/10.1137/1033001","title":"Inertia-Controlling Methods for General Quadratic Programming","display_name":"Inertia-Controlling Methods for General Quadratic Programming","publication_year":1991,"publication_date":"1991-03-01","ids":{"openalex":"https://openalex.org/W1977244564","doi":"https://doi.org/10.1137/1033001","mag":"1977244564"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/1033001","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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://www.ccom.ucsd.edu/~peg/papers/icqp.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003732991","display_name":"Philip E. Gill","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. E. Gill","raw_affiliation_strings":["University of California at San Diego"],"affiliations":[{"raw_affiliation_string":"University of California at San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109312645","display_name":"Walter Murray","orcid":null},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"W. Murray","raw_affiliation_strings":["University of California at San Diego"],"affiliations":[{"raw_affiliation_string":"University of California at San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039807799","display_name":"Michael A. Saunders","orcid":"https://orcid.org/0000-0003-3800-4982"},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. A. Saunders","raw_affiliation_strings":["University of California at San Diego"],"affiliations":[{"raw_affiliation_string":"University of California at San Diego","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103458692","display_name":"Margaret H. Wright","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. H. Wright","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.038,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":96,"citation_normalized_percentile":{"value":0.982122,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":97},"biblio":{"volume":"33","issue":"1","first_page":"1","last_page":"36"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9969,"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"}},"topics":[{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9969,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9967,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9958,"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/hessian-matrix","display_name":"Hessian matrix","score":0.90672916},{"id":"https://openalex.org/keywords/hessian-equation","display_name":"Hessian equation","score":0.42992178}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.90672916},{"id":"https://openalex.org/C110407247","wikidata":"https://www.wikidata.org/wiki/Q122508","display_name":"Inertia","level":2,"score":0.74975896},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.6398224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6223136},{"id":"https://openalex.org/C56828936","wikidata":"https://www.wikidata.org/wiki/Q1752621","display_name":"Sylvester's law of inertia","level":4,"score":0.59217405},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.553395},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.51406085},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.48657978},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4777933},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.44678888},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43117833},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.42992178},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24298769},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23630327},{"id":"https://openalex.org/C54848796","wikidata":"https://www.wikidata.org/wiki/Q339011","display_name":"Symmetric matrix","level":3,"score":0.19285685},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1063492},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06547356},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06018758},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1137/1033001","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":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.491.4882","pdf_url":"http://www.ccom.ucsd.edu/~peg/papers/icqp.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.491.4882","pdf_url":"http://www.ccom.ucsd.edu/~peg/papers/icqp.pdf","source":{"id":"https://openalex.org/S4306400349","display_name":"CiteSeer X (The Pennsylvania State University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130769515","host_organization_name":"Pennsylvania State University","host_organization_lineage":["https://openalex.org/I130769515"],"host_organization_lineage_names":["Pennsylvania State University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":35,"referenced_works":["https://openalex.org/W141418607","https://openalex.org/W143069517","https://openalex.org/W1484908674","https://openalex.org/W1586015540","https://openalex.org/W1968607806","https://openalex.org/W1975326300","https://openalex.org/W1977310057","https://openalex.org/W1982385498","https://openalex.org/W1985400098","https://openalex.org/W1993446440","https://openalex.org/W1997958347","https://openalex.org/W2013737143","https://openalex.org/W2019358363","https://openalex.org/W2021967310","https://openalex.org/W2021982403","https://openalex.org/W2034965940","https://openalex.org/W2036370633","https://openalex.org/W2037909160","https://openalex.org/W2039526985","https://openalex.org/W2051603784","https://openalex.org/W2060753484","https://openalex.org/W2065646793","https://openalex.org/W2079135578","https://openalex.org/W2082709304","https://openalex.org/W2088128439","https://openalex.org/W2090523290","https://openalex.org/W2106353864","https://openalex.org/W2127470768","https://openalex.org/W2127982942","https://openalex.org/W2153738380","https://openalex.org/W2159307101","https://openalex.org/W391646181","https://openalex.org/W4255005337","https://openalex.org/W4285719527","https://openalex.org/W4301216918"],"related_works":["https://openalex.org/W4297791817","https://openalex.org/W4286909496","https://openalex.org/W2989823969","https://openalex.org/W2964019050","https://openalex.org/W2890919253","https://openalex.org/W2755749970","https://openalex.org/W2414981476","https://openalex.org/W2316166864","https://openalex.org/W2120338570","https://openalex.org/W1991833659"],"abstract_inverted_index":{"Active-set":[0],"quadratic":[1],"programming":[2],"(QP)":[3],"methods":[4,57,118],"use":[5],"a":[6,68],"working":[7,33],"set":[8,34],"to":[9,37,49,107],"define":[10,96],"the":[11,18,32,39,42,74,78,82,97,108,125],"search":[12,79,98],"direction":[13,80,99],"and":[14,25,89,100],"multiplier":[15,102],"estimates.":[16],"In":[17],"method":[19],"proposed":[20],"by":[21,77],"Fletcher":[22],"in":[23,26],"1971,":[24],"several":[27],"subsequent":[28],"mathematically":[29],"equivalent":[30],"methods,":[31],"is":[35,46,85,112],"chosen":[36],"control":[38],"inertia":[40],"of":[41,67,114,124],"reduced":[43,83,126],"Hessian,":[44],"which":[45],"never":[47],"permitted":[48],"have":[50],"more":[51],"than":[52],"one":[53],"nonpositive":[54],"eigenvalue.":[55],"(Such":[56],"will":[58],"be":[59],"called":[60],"inertia-controlling.)":[61],"This":[62],"paper":[63],"presents":[64],"an":[65,121],"overview":[66],"generic":[69],"inertia-controlling":[70,117],"QP":[71],"method,":[72],"including":[73],"equations":[75,105],"satisfied":[76],"when":[81],"Hessian":[84,127],"positive":[86],"definite,":[87],"singular":[88],"indefinite.":[90],"Recurrence":[91],"relations":[92],"are":[93],"derived":[94],"that":[95,119],"Lagrange":[101],"vector":[103],"through":[104],"related":[106],"Karush\u2013Kuhn\u2013Tucker":[109],"system.":[110],"Discussion":[111],"included":[113],"connections":[115],"with":[116],"maintain":[120],"explicit":[122],"factorization":[123],"matrix.":[128]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W1977244564","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":7}],"updated_date":"2024-12-13T18:33:21.820814","created_date":"2016-06-24"}