{"id":"https://openalex.org/W4409800312","doi":"https://doi.org/10.1287/moor.2023.0270","title":"Local Maximal Monotonicity in Variational Analysis and Optimization","display_name":"Local Maximal Monotonicity in Variational Analysis and Optimization","publication_year":2025,"publication_date":"2025-04-25","ids":{"openalex":"https://openalex.org/W4409800312","doi":"https://doi.org/10.1287/moor.2023.0270"},"language":"en","primary_location":{"id":"doi:10.1287/moor.2023.0270","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2023.0270","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","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/A5050012100","display_name":"Pham Duy Khanh","orcid":"https://orcid.org/0000-0001-7156-1380"},"institutions":[{"id":"https://openalex.org/I4210104442","display_name":"Ho Chi Minh City University of Education","ror":"https://ror.org/01cs0jg44","country_code":"VN","type":"education","lineage":["https://openalex.org/I4210104442"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Pham Duy Khanh","raw_affiliation_strings":["Group of Analysis and Applied Mathematics, Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City 700000, Vietnam"],"raw_orcid":"https://orcid.org/0000-0001-7156-1380","affiliations":[{"raw_affiliation_string":"Group of Analysis and Applied Mathematics, Department of Mathematics, Ho Chi Minh City University of Education, Ho Chi Minh City 700000, Vietnam","institution_ids":["https://openalex.org/I4210104442"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055132698","display_name":"Vu Vinh Huy Khoa","orcid":"https://orcid.org/0009-0001-9213-1061"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vu Vinh Huy Khoa","raw_affiliation_strings":["Department of Mathematics, Wayne State University, Detroit, Michigan 48202"],"raw_orcid":"https://orcid.org/0009-0001-9213-1061","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, Michigan 48202","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066241737","display_name":"Boris S. Mordukhovich","orcid":"https://orcid.org/0000-0002-6071-6049"},"institutions":[{"id":"https://openalex.org/I185443292","display_name":"Wayne State University","ror":"https://ror.org/01070mq45","country_code":"US","type":"education","lineage":["https://openalex.org/I185443292"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Boris S. Mordukhovich","raw_affiliation_strings":["Department of Mathematics, Wayne State University, Detroit, Michigan 48202"],"raw_orcid":"https://orcid.org/0000-0002-6071-6049","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Wayne State University, Detroit, Michigan 48202","institution_ids":["https://openalex.org/I185443292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050471189","display_name":"Vo Thanh Phat","orcid":"https://orcid.org/0000-0003-1211-8025"},"institutions":[{"id":"https://openalex.org/I24571045","display_name":"University of North Dakota","ror":"https://ror.org/04a5szx83","country_code":"US","type":"education","lineage":["https://openalex.org/I24571045"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Vo Thanh Phat","raw_affiliation_strings":["Department of Mathematics & Statistics, University of North Dakota, Grand Forks, North Dakota 58202"],"raw_orcid":"https://orcid.org/0000-0003-1211-8025","affiliations":[{"raw_affiliation_string":"Department of Mathematics & Statistics, University of North Dakota, Grand Forks, North Dakota 58202","institution_ids":["https://openalex.org/I24571045"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1152,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.87743768,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":98,"max":99},"biblio":{"volume":"51","issue":"2","first_page":"938","last_page":"955"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":1.0,"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":1.0,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/mathematics","display_name":"Mathematics","score":0.8423563838005066},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.7508964538574219},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.5809200406074524},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.518311619758606},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.4608231782913208},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43260428309440613},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.40183407068252563},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3296348750591278},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3251917064189911},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18198072910308838}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8423563838005066},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.7508964538574219},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.5809200406074524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.518311619758606},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.4608231782913208},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43260428309440613},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.40183407068252563},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3296348750591278},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3251917064189911},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18198072910308838},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1287/moor.2023.0270","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2023.0270","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W431634462","https://openalex.org/W1968565992","https://openalex.org/W1996975947","https://openalex.org/W2005669112","https://openalex.org/W2038497950","https://openalex.org/W2042261731","https://openalex.org/W2079004067","https://openalex.org/W2116174279","https://openalex.org/W2132677982","https://openalex.org/W2337364180","https://openalex.org/W2885473730","https://openalex.org/W2922760259","https://openalex.org/W3088611384","https://openalex.org/W3159126638","https://openalex.org/W3197368557","https://openalex.org/W4213229463","https://openalex.org/W4226077233","https://openalex.org/W4245503300","https://openalex.org/W4249513058","https://openalex.org/W4282943332","https://openalex.org/W4381741434","https://openalex.org/W4382809312","https://openalex.org/W4398187116","https://openalex.org/W4409172841"],"related_works":["https://openalex.org/W3118444755","https://openalex.org/W2096782225","https://openalex.org/W2102099143","https://openalex.org/W2142789187","https://openalex.org/W1561544985","https://openalex.org/W1992673508","https://openalex.org/W2116234265","https://openalex.org/W2075980626","https://openalex.org/W2037516588","https://openalex.org/W4249083923"],"abstract_inverted_index":{"The":[0],"paper":[1],"is":[2],"devoted":[3],"to":[4],"a":[5],"systematic":[6],"study":[7],"and":[8,16,29,86,96],"characterizations":[9,36,54],"of":[10,12,37,55,64,70,99],"notions":[11,39,57],"local":[13],"maximal":[14],"monotonicity":[15],"their":[17,30,45],"strong":[18],"counterparts":[19],"for":[20,44],"set-valued":[21],"operators":[22],"that":[23],"appear":[24],"in":[25,49,67],"variational":[26,65],"analysis,":[27],"optimization,":[28],"applications.":[31],"We":[32],"obtain":[33],"novel":[34],"resolvent":[35],"these":[38,56],"together":[40],"with":[41],"efficient":[42],"conditions":[43],"preservation":[46],"under":[47],"summation":[48],"broad":[50],"infinite-dimensional":[51],"settings.":[52],"Further":[53],"are":[58],"derived":[59],"by":[60,78],"using":[61],"generalized":[62],"differentiation":[63],"analysis":[66],"the":[68,79,88],"framework":[69],"Hilbert":[71],"spaces.":[72],"Funding:":[73],"This":[74],"research":[75],"was":[76],"supported":[77],"U.S.":[80],"National":[81],"Science":[82],"Foundation":[83],"[Grants":[84],"DMS-1808978":[85],"DMS-2204519],":[87],"Australian":[89],"Research":[90],"Council":[91],"Discovery":[92],"Project":[93,97],"[Grant":[94,101],"DP-190100555],":[95],"111":[98],"China":[100],"D21024].":[102]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-06-18T10:00:31.954636","created_date":"2025-10-10T00:00:00"}