{"id":"https://openalex.org/W2973458326","doi":"https://doi.org/10.1137/18m1192615","title":"Calmness and the Abadie CQ for Multifunctions and Linear Regularity for a Collection of Closed Sets","display_name":"Calmness and the Abadie CQ for Multifunctions and Linear Regularity for a Collection of Closed Sets","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2973458326","doi":"https://doi.org/10.1137/18m1192615","mag":"2973458326"},"language":"en","primary_location":{"id":"doi:10.1137/18m1192615","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1192615","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/A5102338176","display_name":"Zongshan Shen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zongshan Shen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050520268","display_name":"Jen\u2010Chih Yao","orcid":"https://orcid.org/0000-0001-9041-3375"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jen-Chih Yao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5056391377","display_name":"Xi Yin Zheng","orcid":"https://orcid.org/0000-0002-5314-6471"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xi Yin Zheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7712,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75011873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"3","first_page":"2291","last_page":"2319"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9958999752998352,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/calmness","display_name":"Calmness","score":0.9631572961807251},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8670587539672852},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4950803816318512},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43559902906417847}],"concepts":[{"id":"https://openalex.org/C2778712213","wikidata":"https://www.wikidata.org/wiki/Q20740046","display_name":"Calmness","level":2,"score":0.9631572961807251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8670587539672852},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4950803816318512},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43559902906417847},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C118552586","wikidata":"https://www.wikidata.org/wiki/Q7867","display_name":"Psychiatry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1192615","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1192615","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":[{"score":0.4699999988079071,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G2415924013","display_name":null,"funder_award_id":"11771384","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8754812133","display_name":null,"funder_award_id":"108-2115-M-039-005-MY3","funder_id":"https://openalex.org/F4320321540","funder_display_name":"Ministry of Science and Technology of the People's Republic of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321540","display_name":"Ministry of Science and Technology of the People's Republic of China","ror":"https://ror.org/027s68j25"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W952611802","https://openalex.org/W1586663846","https://openalex.org/W1877455765","https://openalex.org/W1990935327","https://openalex.org/W1991203806","https://openalex.org/W1994724562","https://openalex.org/W2008195537","https://openalex.org/W2010083959","https://openalex.org/W2014715559","https://openalex.org/W2018775338","https://openalex.org/W2020167116","https://openalex.org/W2028324692","https://openalex.org/W2033316062","https://openalex.org/W2033474604","https://openalex.org/W2033511209","https://openalex.org/W2041880818","https://openalex.org/W2047483985","https://openalex.org/W2051462210","https://openalex.org/W2052059821","https://openalex.org/W2064650029","https://openalex.org/W2068350722","https://openalex.org/W2072822417","https://openalex.org/W2075706482","https://openalex.org/W2081600571","https://openalex.org/W2094647511","https://openalex.org/W2116407586","https://openalex.org/W2136171910","https://openalex.org/W2137159907","https://openalex.org/W2150140216"],"related_works":["https://openalex.org/W2358490822","https://openalex.org/W3086329158","https://openalex.org/W4286813019","https://openalex.org/W3011250038","https://openalex.org/W2131815933","https://openalex.org/W2946213799","https://openalex.org/W2036833017","https://openalex.org/W2079252788","https://openalex.org/W3030155790","https://openalex.org/W2046807944"],"abstract_inverted_index":{"In":[0,33],"contrast":[1],"to":[2,27,127],"many":[3],"existing":[4,125],"results":[5,126],"on":[6],"calmness":[7,74,77],"(metric":[8],"subregularity)":[9],"of":[10,35,64,78,86,103],"multifunctions":[11,79],"established":[12],"by":[13],"using":[14],"dual":[15],"notions":[16],"like":[17],"the":[18,36,48,54,62,65,81,129,132],"normal":[19],"cones":[20],"and":[21,40,46,53,75,89,109,114,122],"coderivatives,":[22],"this":[23],"paper":[24],"is":[25],"devoted":[26],"provide":[28],"primal":[29,71,112],"issues":[30],"for":[31,57,73,97,117],"calmness.":[32],"terms":[34],"Bouligand":[37],"tangent":[38,42],"cone":[39],"Clarke":[41],"cone,":[43],"we":[44,68,93],"introduce":[45],"study":[47],"Abadie":[49],"constraint":[50],"qualification":[51],"(ACQ)":[52],"strong":[55,66,76],"ACQ":[56],"a":[58,98],"nonconvex":[59,130],"multifunction.":[60],"With":[61],"help":[63],"ACQ,":[67],"establish":[69,110],"several":[70],"characterizations":[72],"with":[80],"Shapiro":[82],"property":[83],"(an":[84],"extension":[85],"both":[87],"convexity":[88],"smoothness).":[90],"As":[91],"applications,":[92],"consider":[94],"linear":[95,118],"regularity":[96],"finite":[99],"or":[100,131],"infinite":[101,133],"collection":[102],"closed":[104],"(not":[105],"necessarily":[106],"convex)":[107],"sets":[108],"some":[111,124],"sufficient":[113],"necessary":[115],"conditions":[116],"regularity,":[119],"which":[120],"extend":[121],"improve":[123],"either":[128],"index":[134],"set":[135],"case.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
