{"id":"https://openalex.org/W1993708577","doi":"https://doi.org/10.1137/s0363012900374816","title":"Necessary Suboptimality and Optimality Conditions via Variational Principles","display_name":"Necessary Suboptimality and Optimality Conditions via Variational Principles","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1993708577","doi":"https://doi.org/10.1137/s0363012900374816","mag":"1993708577"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012900374816","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012900374816","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and 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/A5066241737","display_name":"Boris S. Mordukhovich","orcid":"https://orcid.org/0000-0002-6071-6049"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boris S. Mordukhovich","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5102878843","display_name":"Bingwu Wang","orcid":"https://orcid.org/0000-0002-1154-1860"},"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":"Bingwu Wang","raw_affiliation_strings":["Wayne State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Wayne State University","institution_ids":["https://openalex.org/I185443292"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.8827,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.96936636,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"41","issue":"2","first_page":"623","last_page":"640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9995999932289124,"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":0.9995999932289124,"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":0.995199978351593,"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":0.9873999953269958,"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/subderivative","display_name":"Subderivative","score":0.8505430221557617},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8105387687683105},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.7848430871963501},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.7077511548995972},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6133478283882141},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5721686482429504},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.5091819167137146},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44289955496788025},{"id":"https://openalex.org/keywords/variational-principle","display_name":"Variational principle","score":0.43623924255371094},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4124414324760437},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.21892741322517395},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.20774054527282715},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16805952787399292}],"concepts":[{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.8505430221557617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8105387687683105},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.7848430871963501},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.7077511548995972},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6133478283882141},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5721686482429504},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.5091819167137146},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44289955496788025},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.43623924255371094},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4124414324760437},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.21892741322517395},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.20774054527282715},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16805952787399292},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0363012900374816","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012900374816","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5600000023841858,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W121895575","https://openalex.org/W161756625","https://openalex.org/W1492700492","https://openalex.org/W1569878307","https://openalex.org/W1601960826","https://openalex.org/W1644964607","https://openalex.org/W1775014066","https://openalex.org/W1971296668","https://openalex.org/W1972577527","https://openalex.org/W1977750299","https://openalex.org/W1993702196","https://openalex.org/W2004246387","https://openalex.org/W2028253364","https://openalex.org/W2033623440","https://openalex.org/W2049120749","https://openalex.org/W2056503788","https://openalex.org/W2065139676","https://openalex.org/W2065171653","https://openalex.org/W2071268390","https://openalex.org/W2110041091","https://openalex.org/W2112277685","https://openalex.org/W2140729585","https://openalex.org/W2248544343","https://openalex.org/W2653106040","https://openalex.org/W2798574506","https://openalex.org/W2955198501","https://openalex.org/W4249513058","https://openalex.org/W4251348386","https://openalex.org/W4299815621","https://openalex.org/W4301056270"],"related_works":["https://openalex.org/W2563326832","https://openalex.org/W1995521228","https://openalex.org/W1564508692","https://openalex.org/W1993708577","https://openalex.org/W2040739535","https://openalex.org/W2596782428","https://openalex.org/W2142789187","https://openalex.org/W1967128235","https://openalex.org/W2007576447","https://openalex.org/W2101492045"],"abstract_inverted_index":{"The":[0],"paper":[1],"aims":[2],"to":[3,16,56,61],"develop":[4],"some":[5],"basic":[6],"principles":[7,53],"and":[8,19,54,86,115],"tools":[9],"of":[10,40,51,103,121,128],"nonconvex":[11],"variational":[12,34,52,68,113],"analysis":[13,114],"with":[14,83],"applications":[15,60],"necessary":[17,73,129],"suboptimality":[18],"optimality":[20,130],"conditions":[21,74,131],"for":[22,59,75,132],"constrained":[23,134],"optimization":[24,81],"problems":[25,82,135],"in":[26,78,89,111,136,143],"infinite":[27,137],"dimensions.":[28],"We":[29],"establish":[30,96],"a":[31,37,119],"certain":[32],"subdifferential":[33,67],"principle":[35],"as":[36],"new":[38,72],"characterization":[39],"Asplund":[41,90],"spaces.":[42,91],"This":[43],"result":[44],"is":[45],"different":[46],"from":[47],"conventional":[48],"support":[49],"forms":[50,127],"appears":[55],"be":[57],"convenient":[58],"nonsmooth":[62,80,133],"optimization.":[63],"Based":[64],"on":[65],"the":[66,97],"principle,":[69],"we":[70,95,124],"obtain":[71],"suboptimal":[76],"solutions":[77],"general":[79],"equality,":[84],"inequality,":[85],"set":[87],"constraints":[88],"In":[92],"this":[93],"way":[94],"so-called":[98],"sequential":[99],"normal":[100],"compactness":[101],"properties":[102],"constraint":[104],"sets":[105],"that":[106,144],"play":[107],"an":[108],"essential":[109],"role":[110],"infinite-dimensional":[112],"its":[116],"applications.":[117],"As":[118],"by-product":[120],"our":[122],"approach,":[123],"derive":[125],"various":[126],"dimensions,":[138],"which":[139],"extend":[140],"known":[141],"results":[142],"direction.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}