{"id":"https://openalex.org/W4380879525","doi":"https://doi.org/10.1137/22m1512454","title":"Fr\u00e9chet Second-Order Subdifferentials of Lagrangian Functions and Optimality Conditions","display_name":"Fr\u00e9chet Second-Order Subdifferentials of Lagrangian Functions and Optimality Conditions","publication_year":2023,"publication_date":"2023-06-16","ids":{"openalex":"https://openalex.org/W4380879525","doi":"https://doi.org/10.1137/22m1512454"},"language":"en","primary_location":{"id":"doi:10.1137/22m1512454","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1512454","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/A5088791808","display_name":"Duong Thi Viet An","orcid":"https://orcid.org/0000-0003-1822-4929"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Duong Thi Viet An","raw_affiliation_strings":["School of Management, Hangzhou Dianzi University, Hangzhou 310018, China, and Department of Mathematics and Informatics, Thai Nguyen University of Sciences, Thai Nguyen 25000, Vietnam"],"affiliations":[{"raw_affiliation_string":"School of Management, Hangzhou Dianzi University, Hangzhou 310018, China, and Department of Mathematics and Informatics, Thai Nguyen University of Sciences, Thai Nguyen 25000, Vietnam","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014614476","display_name":"Hong\u2010Kun Xu","orcid":"https://orcid.org/0000-0002-2035-2105"},"institutions":[{"id":"https://openalex.org/I50760025","display_name":"Hangzhou Dianzi University","ror":"https://ror.org/0576gt767","country_code":"CN","type":"education","lineage":["https://openalex.org/I50760025"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hong-Kun Xu","raw_affiliation_strings":["School of Science, Hangzhou Dianzi University, Hangzhou 310018, China"],"affiliations":[{"raw_affiliation_string":"School of Science, Hangzhou Dianzi University, Hangzhou 310018, China","institution_ids":["https://openalex.org/I50760025"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034470275","display_name":"Nguyen Dong Yen","orcid":null},"institutions":[{"id":"https://openalex.org/I70349855","display_name":"Vietnam Academy of Science and Technology","ror":"https://ror.org/02wsd5p50","country_code":"VN","type":"funder","lineage":["https://openalex.org/I70349855"]},{"id":"https://openalex.org/I4210148301","display_name":"Institute of Mathematics","ror":"https://ror.org/04jr71r83","country_code":"VN","type":"facility","lineage":["https://openalex.org/I4210148301","https://openalex.org/I70349855"]}],"countries":["VN"],"is_corresponding":false,"raw_author_name":"Nguyen Dong Yen","raw_affiliation_strings":["Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi 10307, Vietnam"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi 10307, Vietnam","institution_ids":["https://openalex.org/I70349855","https://openalex.org/I4210148301"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5088791808"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2102,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81745358,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"33","issue":"2","first_page":"766","last_page":"784"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9988999962806702,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9973999857902527,"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":0.8947345018386841},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.736749529838562},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.659699559211731},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.5995533466339111},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5841335654258728},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4866848587989807},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.48581576347351074},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.48322686553001404},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4702412486076355},{"id":"https://openalex.org/keywords/calculus-of-variations","display_name":"Calculus of variations","score":0.419587105512619},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28930148482322693},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.2414490282535553},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.1456938087940216},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.083342045545578}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8947345018386841},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.736749529838562},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.659699559211731},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.5995533466339111},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5841335654258728},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4866848587989807},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.48581576347351074},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.48322686553001404},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4702412486076355},{"id":"https://openalex.org/C97985569","wikidata":"https://www.wikidata.org/wiki/Q216861","display_name":"Calculus of variations","level":2,"score":0.419587105512619},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28930148482322693},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2414490282535553},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.1456938087940216},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.083342045545578},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1512454","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1512454","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1909650407","display_name":null,"funder_award_id":"101.01-2018.308","funder_id":"https://openalex.org/F4320309617","funder_display_name":"National Foundation for Science and Technology Development"},{"id":"https://openalex.org/G389875158","display_name":null,"funder_award_id":"NVCC01.07/22-23","funder_id":"https://openalex.org/F4320313223","funder_display_name":"Vietnam Academy of Science and Technology"},{"id":"https://openalex.org/G5372072380","display_name":null,"funder_award_id":"U1811461","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6366594956","display_name":null,"funder_award_id":"DP200100124","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"},{"id":"https://openalex.org/F4320313223","display_name":"Vietnam Academy of Science and Technology","ror":"https://ror.org/02wsd5p50"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W591794949","https://openalex.org/W1601741115","https://openalex.org/W1972451512","https://openalex.org/W1983871704","https://openalex.org/W1990592299","https://openalex.org/W1993613781","https://openalex.org/W2000120257","https://openalex.org/W2001381910","https://openalex.org/W2003540223","https://openalex.org/W2020489358","https://openalex.org/W2027449074","https://openalex.org/W2034492412","https://openalex.org/W2034902472","https://openalex.org/W2041037772","https://openalex.org/W2042153418","https://openalex.org/W2045497213","https://openalex.org/W2045544449","https://openalex.org/W2045940260","https://openalex.org/W2100384283","https://openalex.org/W2116817647","https://openalex.org/W2122856151","https://openalex.org/W2494957067","https://openalex.org/W2595897327","https://openalex.org/W2617507642","https://openalex.org/W2885473730","https://openalex.org/W3047218426","https://openalex.org/W3135986428","https://openalex.org/W3170904530","https://openalex.org/W3173142515","https://openalex.org/W3216123028","https://openalex.org/W4231758816","https://openalex.org/W4232376992","https://openalex.org/W4244641530","https://openalex.org/W4248283078","https://openalex.org/W4249513058","https://openalex.org/W4250028192","https://openalex.org/W4299439662"],"related_works":["https://openalex.org/W2563326832","https://openalex.org/W1995521228","https://openalex.org/W1993708577","https://openalex.org/W2040739535","https://openalex.org/W2596782428","https://openalex.org/W2972051521","https://openalex.org/W2007576447","https://openalex.org/W4288243393","https://openalex.org/W3047218426","https://openalex.org/W4301447736"],"abstract_inverted_index":{".We":[0],"establish":[1],"some":[2],"new":[3],"results":[4,57],"on":[5,65],"second-order":[6,42,71],"(necessary":[7],"and":[8,59],"sufficient)":[9],"optimality":[10,74,77],"conditions":[11],"for":[12],"minimization":[13],"problems":[14],"with":[15],"abstract":[16],"constraints":[17],"in":[18],"infinite-dimensional":[19],"spaces,":[20],"where":[21],"the":[22,37,48,52],"objective":[23],"functions":[24],"are":[25],"only":[26],"assumed":[27],"to":[28,47],"be":[29],"\\(C^1\\)":[30],"-smooth.":[31],"For":[32],"doing":[33],"so,":[34],"we":[35],"apply":[36],"concept":[38],"of":[39,51],"Fr\u00e9chet":[40],"(regular)":[41],"subdifferential":[43],"from":[44],"variational":[45],"analysis":[46],"Lagrangian":[49],"function":[50],"problem":[53,64],"under":[54],"investigation.":[55],"Our":[56],"extend":[58],"refine":[60],"several":[61],"existing":[62],"ones.Keywordsminimization":[63],"Banach":[66],"spacescone":[67],"constrainttangent":[68],"setLagrange":[69],"multiplierFr\u00e9chet":[70],"subdifferentialsecond-order":[72],"necessary":[73],"conditionsecond-order":[75],"sufficient":[76],"conditionMSC":[78],"codes90C3049K2749J5390C5626A27":[79]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}