{"id":"https://openalex.org/W2797479470","doi":"https://doi.org/10.1137/18m1181602","title":"Intrinsic Formulation of KKT Conditions and Constraint Qualifications on Smooth Manifolds","display_name":"Intrinsic Formulation of KKT Conditions and Constraint Qualifications on Smooth Manifolds","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2797479470","doi":"https://doi.org/10.1137/18m1181602","mag":"2797479470"},"language":"en","primary_location":{"id":"doi:10.1137/18m1181602","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1181602","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1804.06214","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106698931","display_name":"Ronny Bergmann","orcid":"https://orcid.org/0000-0001-8342-7218"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ronny Bergmann","raw_affiliation_strings":["Technische Universit\u00e4t Chemnitz, Faculty of Mathematics, Professorship Numeri-cal Mathematics (Partial Differential Equations), D-09107 Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Chemnitz, Faculty of Mathematics, Professorship Numeri-cal Mathematics (Partial Differential Equations), D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070215713","display_name":"Roland Herzog","orcid":"https://orcid.org/0000-0003-2164-6575"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Roland Herzog","raw_affiliation_strings":["Technische Universit\u00e4t Chemnitz, Faculty of Mathematics, Professorship Numeri-cal Mathematics (Partial Differential Equations), D-09107 Chemnitz, Germany"],"raw_orcid":"https://orcid.org/0000-0003-2164-6575","affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Chemnitz, Faculty of Mathematics, Professorship Numeri-cal Mathematics (Partial Differential Equations), D-09107 Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I2610724"],"apc_list":null,"apc_paid":null,"fwci":2.8422,"has_fulltext":true,"cited_by_count":52,"citation_normalized_percentile":{"value":0.91376189,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"29","issue":"4","first_page":"2423","last_page":"2444"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9979000091552734,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9936000108718872,"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/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.960087776184082},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8337634801864624},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.8316066265106201},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.7558876276016235},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.5558494329452515},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.494655579328537},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47930851578712463},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.4626871347427368},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"Constrained optimization","score":0.41294392943382263},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40120843052864075},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33835721015930176},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11238133907318115},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08256492018699646}],"concepts":[{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.960087776184082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8337634801864624},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.8316066265106201},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.7558876276016235},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.5558494329452515},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.494655579328537},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47930851578712463},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.4626871347427368},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.41294392943382263},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40120843052864075},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33835721015930176},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11238133907318115},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08256492018699646},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1181602","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1181602","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:arXiv.org:1804.06214","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1804.06214","pdf_url":"https://arxiv.org/pdf/1804.06214","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1804.06214","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1804.06214","pdf_url":"https://arxiv.org/pdf/1804.06214","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[{"score":0.6100000143051147,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G1680711539","display_name":null,"funder_award_id":"BE5888/2-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G188083318","display_name":null,"funder_award_id":"SPP-1962","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8269064541","display_name":null,"funder_award_id":"HE 6077/10-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W75469790","https://openalex.org/W100063776","https://openalex.org/W596136856","https://openalex.org/W648446685","https://openalex.org/W1525296983","https://openalex.org/W1555268757","https://openalex.org/W1557324374","https://openalex.org/W1587069887","https://openalex.org/W1970946112","https://openalex.org/W1978037315","https://openalex.org/W2007943266","https://openalex.org/W2021667451","https://openalex.org/W2021974634","https://openalex.org/W2046019310","https://openalex.org/W2048755319","https://openalex.org/W2061455579","https://openalex.org/W2063589154","https://openalex.org/W2109409043","https://openalex.org/W2110662303","https://openalex.org/W2258202344","https://openalex.org/W2346678144","https://openalex.org/W2487202609","https://openalex.org/W2611293703","https://openalex.org/W2756161774","https://openalex.org/W2912158546","https://openalex.org/W2962777248","https://openalex.org/W2963704853","https://openalex.org/W2964029293","https://openalex.org/W2999060662","https://openalex.org/W3000651840","https://openalex.org/W3098206065","https://openalex.org/W3098483780","https://openalex.org/W3142379583","https://openalex.org/W4205293427","https://openalex.org/W4234534407","https://openalex.org/W4235358177","https://openalex.org/W4236506220","https://openalex.org/W4251507077","https://openalex.org/W4292023735","https://openalex.org/W4293203252","https://openalex.org/W4301014524"],"related_works":["https://openalex.org/W4313491493","https://openalex.org/W2806604749","https://openalex.org/W4381489587","https://openalex.org/W4379919368","https://openalex.org/W3173427300","https://openalex.org/W3029600049","https://openalex.org/W2593574046","https://openalex.org/W4210398350","https://openalex.org/W4299317744","https://openalex.org/W2951068194"],"abstract_inverted_index":{"Karush--Kuhn--Tucker":[0],"(KKT)":[1],"conditions":[2],"for":[3],"equality":[4],"and":[5,32,39,58],"inequality":[6],"constrained":[7,74],"optimization":[8],"problems":[9],"on":[10,79],"smooth":[11],"manifolds":[12],"are":[13,22,36,64],"formulated.":[14],"Under":[15],"the":[16,40,59,68,80],"Guignard":[17],"constraint":[18,34,56],"qualification,":[19],"local":[20],"minimizers":[21],"shown":[23],"to":[24],"admit":[25],"Lagrange":[26,62],"multipliers.":[27],"The":[28,73],"linear":[29],"independence,":[30],"Mangasarian--Fromovitz,":[31],"Abadie":[33],"qualifications":[35,57],"also":[37],"formulated,":[38],"chain":[41],"\u201cLICQ":[42],"implies":[43,45,47],"MFCQ":[44],"ACQ":[46],"GCQ\u201d":[48],"is":[49],"proved.":[50],"Moreover,":[51],"classical":[52],"connections":[53],"between":[54],"these":[55],"set":[60],"of":[61,77],"multipliers":[63],"established,":[65],"which":[66],"parallel":[67],"results":[69],"in":[70],"Euclidean":[71],"space.":[72],"Riemannian":[75],"center":[76],"mass":[78],"sphere":[81],"serves":[82],"as":[83],"an":[84],"illustrating":[85],"numerical":[86],"example.":[87]},"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2018-04-24T00:00:00"}