{"id":"https://openalex.org/W4304944461","doi":"https://doi.org/10.1090/mcom/3799","title":"A novel augmented Lagrangian method of multipliers for optimization with general inequality constraints","display_name":"A novel augmented Lagrangian method of multipliers for optimization with general inequality constraints","publication_year":2022,"publication_date":"2022-10-13","ids":{"openalex":"https://openalex.org/W4304944461","doi":"https://doi.org/10.1090/mcom/3799"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3799","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3799","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5100461515","display_name":"Xinwei Liu","orcid":"https://orcid.org/0000-0002-9829-3395"},"institutions":[{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xin-Wei Liu","raw_affiliation_strings":["Institute of Mathematics, Hebei University of Technology, Tianjin 300401, People\u00e2\u0080\u0099s Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Hebei University of Technology, Tianjin 300401, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I184843921"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109187979","display_name":"Yu\u2010Hong Dai","orcid":"https://orcid.org/0000-0002-6932-9512"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu-Hong Dai","raw_affiliation_strings":["Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People\u00e2\u0080\u0099s Republic of China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People\u00e2\u0080\u0099s Republic of China","School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People\u00e2\u0080\u0099s Republic of China","Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People\u00e2\u0080\u0099s Republic of China"],"affiliations":[{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People\u00e2\u0080\u0099s Republic of China; and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I4210165038"]},{"raw_affiliation_string":"School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210165038"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057587509","display_name":"Yakui Huang","orcid":"https://orcid.org/0000-0001-6149-3222"},"institutions":[{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ya-Kui Huang","raw_affiliation_strings":["Institute of Mathematics, Hebei University of Technology, Tianjin 300401, People\u00e2\u0080\u0099s Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Hebei University of Technology, Tianjin 300401, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I184843921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100618850","display_name":"Jie Sun","orcid":"https://orcid.org/0000-0001-5611-1672"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I184843921","display_name":"Hebei University of Technology","ror":"https://ror.org/018hded08","country_code":"CN","type":"education","lineage":["https://openalex.org/I184843921"]}],"countries":["CN","SG"],"is_corresponding":false,"raw_author_name":"Jie Sun","raw_affiliation_strings":["Institute of Mathematics, Hebei University of Technology, Tianjin 300401, People\u00e2\u0080\u0099s Republic of China; and School of Business, National University of Singapore, Singapore 119245, Singapore","Institute of Mathematics, Hebei University of Technology, Tianjin 300401, People\u00e2\u0080\u0099s Republic of China","School of Business, National University of Singapore, Singapore 119245, Singapore"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Hebei University of Technology, Tianjin 300401, People\u00e2\u0080\u0099s Republic of China; and School of Business, National University of Singapore, Singapore 119245, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Institute of Mathematics, Hebei University of Technology, Tianjin 300401, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I184843921"]},{"raw_affiliation_string":"School of Business, National University of Singapore, Singapore 119245, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100461515"],"corresponding_institution_ids":["https://openalex.org/I184843921"],"apc_list":null,"apc_paid":null,"fwci":4.0186,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.9462831,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"92","issue":"341","first_page":"1301","last_page":"1330"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.994700014591217,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9923999905586243,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.915808916091919},{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.858025074005127},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8071039319038391},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6591461896896362},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6450816988945007},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.4810757637023926},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.48014041781425476},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.46083810925483704},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4241471290588379},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.42031723260879517},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.415189653635025},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"Constrained optimization","score":0.41300705075263977},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4113450050354004},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11505591869354248}],"concepts":[{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.915808916091919},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.858025074005127},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8071039319038391},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6591461896896362},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6450816988945007},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.4810757637023926},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.48014041781425476},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.46083810925483704},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4241471290588379},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.42031723260879517},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.415189653635025},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.41300705075263977},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4113450050354004},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11505591869354248},{"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/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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/mcom/3799","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3799","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5799999833106995,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W646582900","https://openalex.org/W1482453036","https://openalex.org/W1970065252","https://openalex.org/W1973889396","https://openalex.org/W1974159169","https://openalex.org/W1986490170","https://openalex.org/W1987995897","https://openalex.org/W1991182684","https://openalex.org/W1992688650","https://openalex.org/W1998150031","https://openalex.org/W1999356624","https://openalex.org/W2005865517","https://openalex.org/W2006449495","https://openalex.org/W2023122478","https://openalex.org/W2025644537","https://openalex.org/W2042204689","https://openalex.org/W2042613327","https://openalex.org/W2048221927","https://openalex.org/W2050267927","https://openalex.org/W2057624533","https://openalex.org/W2058194880","https://openalex.org/W2058708460","https://openalex.org/W2061646356","https://openalex.org/W2084478514","https://openalex.org/W2091442156","https://openalex.org/W2105693192","https://openalex.org/W2125410188","https://openalex.org/W2135779729","https://openalex.org/W2155865164","https://openalex.org/W2157570139","https://openalex.org/W2299710719","https://openalex.org/W2345986964","https://openalex.org/W2791183871","https://openalex.org/W2818269273","https://openalex.org/W2950500548","https://openalex.org/W2962956186","https://openalex.org/W2971646932","https://openalex.org/W3012080241","https://openalex.org/W3015765855","https://openalex.org/W4252626574","https://openalex.org/W4252894371","https://openalex.org/W4256110696","https://openalex.org/W4293775970","https://openalex.org/W4293860233"],"related_works":["https://openalex.org/W4386916233","https://openalex.org/W2360271985","https://openalex.org/W2131718214","https://openalex.org/W4298347182","https://openalex.org/W2408672909","https://openalex.org/W2155865164","https://openalex.org/W2783836771","https://openalex.org/W2002987466","https://openalex.org/W120058203","https://openalex.org/W2615021531"],"abstract_inverted_index":{"We":[0],"introduce":[1],"a":[2,17,51,60,72,109,158,163,172],"twice":[3,110],"differentiable":[4,112],"augmented":[5,33,37,56,64],"Lagrangian":[6,38,65],"for":[7,79,223],"nonlinear":[8,184],"optimization":[9,80,114,224],"with":[10,76,81,221,225],"general":[11],"inequality":[12,82,101],"constraints":[13],"and":[14,58,66,91,123,131],"show":[15],"that":[16,144],"strict":[18,28],"local":[19,29,132],"minimizer":[20],"of":[21,31,40,53,62,100,183,196,202],"the":[22,32,54,63,67,88,98,145,168,187,199,203,215],"original":[23],"problem":[24,188],"is":[25,43,48,59,142,171,189,194,210,219],"an":[26,179],"approximate":[27],"solution":[30],"Lagrangian.":[34],"A":[35],"novel":[36],"method":[39,47,107,147,153,193],"multipliers":[41],"(ALM)":[42],"then":[44],"presented.":[45],"Our":[46],"originated":[49],"from":[50],"generalization":[52],"Hestenes-Powell":[55],"Lagrangian,":[57],"combination":[61],"interior-point":[68],"technique.":[69],"It":[70,174],"shares":[71],"similar":[73],"algorithmic":[74],"framework":[75],"existing":[77],"ALMs":[78,222],"constraints,":[83],"but":[84],"it":[85,141,209],"can":[86],"use":[87],"second":[89],"derivatives":[90],"does":[92],"not":[93],"depend":[94],"on":[95,97,116,232],"projections":[96],"set":[99],"constraints.":[102,227],"In":[103],"each":[104],"iteration,":[105],"our":[106,192,239],"solves":[108],"continuously":[111],"unconstrained":[113],"subproblem":[115],"primal":[117],"variables.":[118],"The":[119,129,152,228],"dual":[120],"iterates,":[121],"penalty":[122],"smoothing":[124],"parameters":[125],"are":[126,134],"updated":[127],"adaptively.":[128],"global":[130,150],"convergence":[133],"analyzed.":[135],"Without":[136],"assuming":[137],"any":[138],"constraint":[139],"qualification,":[140],"proved":[143],"proposed":[146],"has":[148],"strong":[149],"convergence.":[151],"may":[154,175],"converge":[155,177],"to":[156,178,214],"either":[157],"Karush-Kuhn-Tucker":[159],"(KKT)":[160],"point":[161,166,170,182],"or":[162],"singular":[164],"stationary":[165,181],"when":[167,186],"converging":[169],"minimizer.":[173],"also":[176],"infeasible":[180],"program":[185],"infeasible.":[190],"Furthermore,":[191],"capable":[195],"rapidly":[197],"detecting":[198],"possible":[200],"infeasibility":[201],"solved":[204],"problem.":[205],"Under":[206],"suitable":[207],"conditions,":[208],"locally":[211],"linearly":[212],"convergent":[213],"KKT":[216],"point,":[217],"which":[218],"consistent":[220],"equality":[226],"preliminary":[229],"numerical":[230],"experiments":[231],"some":[233],"small":[234],"benchmark":[235],"test":[236],"problems":[237],"demonstrate":[238],"theoretical":[240],"results.":[241]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
