{"id":"https://openalex.org/W1991359458","doi":"https://doi.org/10.1137/s1052623497326629","title":"On the Constant Positive Linear Dependence Condition and Its Application to SQP Methods","display_name":"On the Constant Positive Linear Dependence Condition and Its Application to SQP Methods","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1991359458","doi":"https://doi.org/10.1137/s1052623497326629","mag":"1991359458"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623497326629","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623497326629","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Liqun Qi","raw_affiliation_strings":["University Of New south Wales"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University Of New south Wales","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100938087","display_name":"Zengxin Wei","orcid":null},"institutions":[{"id":"https://openalex.org/I150807315","display_name":"Guangxi University","ror":"https://ror.org/02c9qn167","country_code":"CN","type":"education","lineage":["https://openalex.org/I150807315"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zengxin Wei","raw_affiliation_strings":["GUANGXI UNIVERSITY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"GUANGXI UNIVERSITY","institution_ids":["https://openalex.org/I150807315"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7447,"has_fulltext":false,"cited_by_count":201,"citation_normalized_percentile":{"value":0.95088968,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"10","issue":"4","first_page":"963","last_page":"981"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9962999820709229,"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/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.9758573770523071},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6834920644760132},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5944211483001709},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.5373176336288452},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5194615721702576},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5125482082366943},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.505943238735199},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.34889209270477295},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14635193347930908}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.9758573770523071},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6834920644760132},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5944211483001709},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.5373176336288452},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5194615721702576},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5125482082366943},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.505943238735199},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.34889209270477295},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14635193347930908},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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:10.1137/s1052623497326629","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623497326629","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.829.5670","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.829.5670","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://ira.lib.polyu.edu.hk/bitstream/10397/4759/1/Qi_Constant_positive_linear.pdf","raw_type":"text"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/4759","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/4759","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.550000011920929}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W19099988","https://openalex.org/W69179662","https://openalex.org/W189973867","https://openalex.org/W217831350","https://openalex.org/W1490084264","https://openalex.org/W1494436834","https://openalex.org/W1522222833","https://openalex.org/W1537335979","https://openalex.org/W1573176827","https://openalex.org/W1607072065","https://openalex.org/W1973963981","https://openalex.org/W1974546081","https://openalex.org/W1980428414","https://openalex.org/W1980782931","https://openalex.org/W1993647205","https://openalex.org/W2013315229","https://openalex.org/W2014746566","https://openalex.org/W2022745738","https://openalex.org/W2030184503","https://openalex.org/W2037360107","https://openalex.org/W2042725681","https://openalex.org/W2057875970","https://openalex.org/W2059589283","https://openalex.org/W2061555414","https://openalex.org/W2079340989","https://openalex.org/W2080474145","https://openalex.org/W2082746403","https://openalex.org/W2089856363","https://openalex.org/W2091561969","https://openalex.org/W2093404847","https://openalex.org/W2097564522","https://openalex.org/W2124959855","https://openalex.org/W2218983664","https://openalex.org/W2485320594"],"related_works":["https://openalex.org/W1981158318","https://openalex.org/W4367186753","https://openalex.org/W4288092242","https://openalex.org/W2164754346","https://openalex.org/W2980744749","https://openalex.org/W2159682255","https://openalex.org/W4378551200","https://openalex.org/W2610069809","https://openalex.org/W4206704743","https://openalex.org/W2108325790"],"abstract_inverted_index":{"In":[0],"this":[1,141],"paper,":[2],"we":[3,91,132],"introduce":[4],"a":[5,31,35,43,54,77,122,137,147],"constant":[6,23],"positive":[7],"linear":[8,153],"dependence":[9],"condition":[10,123,148],"(CPLD),":[11],"which":[12],"is":[13,42,67],"weaker":[14,125,150],"than":[15,126,151],"the":[16,22,47,58,61,85,88,97,119,127,144,152],"Mangasarian--Fromovitz":[17,128],"constraint":[18,25,129,155],"qualification":[19,26],"(MFCQ)":[20],"and":[21,60,87,104,121,131,146],"rank":[24],"(CRCQ).":[27],"We":[28,51,72,113],"show":[29,52],"that":[30,53],"limit":[32],"point":[33,45,56],"of":[34,37,76,136,140],"sequence":[36],"approximating":[38],"Karush--Kuhn--Tucker":[39],"(KKT)":[40],"points":[41],"KKT":[44,55,70],"if":[46],"CPLD":[48,59,86],"holds":[49],"there.":[50],"satisfying":[57],"strong":[62],"second-order":[63],"sufficiency":[64],"conditions":[65],"(SSOSC)":[66],"an":[68],"isolated":[69],"point.":[71],"then":[73],"establish":[74,114],"convergence":[75,117,135],"general":[78],"sequential":[79],"quadratical":[80],"programming":[81],"(SQP)":[82],"method":[83,100],"under":[84,118,143],"SSOSC.":[89],"Finally,":[90],"apply":[92],"these":[93],"results":[94],"to":[95],"analyze":[96],"feasible":[98],"SQP":[99],"proposed":[101],"by":[102],"Panier":[103],"Tits":[105],"in":[106],"1993":[107],"for":[108],"inequality":[109],"constrained":[110],"optimization":[111],"problems.":[112],"its":[115],"global":[116],"SSOSC":[120,145],"slightly":[124,149],"qualification,":[130],"prove":[133],"superlinear":[134],"modified":[138],"version":[139],"algorithm":[142],"independence":[154],"qualification.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":13},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
