{"id":"https://openalex.org/W2018290510","doi":"https://doi.org/10.1137/130941493","title":"The Dual Normal CHIP and Linear Regularity for Infinite Systems of Convex Sets in Banach Spaces","display_name":"The Dual Normal CHIP and Linear Regularity for Infinite Systems of Convex Sets in Banach Spaces","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2018290510","doi":"https://doi.org/10.1137/130941493","mag":"2018290510"},"language":"en","primary_location":{"id":"doi:10.1137/130941493","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130941493","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/A5100424917","display_name":"Chong Li","orcid":"https://orcid.org/0000-0001-7097-4220"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chong Li","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5040074886","display_name":"K. F. Ng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. F. Ng","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100424917"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7122,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.70931479,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"24","issue":"3","first_page":"1075","last_page":"1101"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9979000091552734,"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8706473112106323},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7364498376846313},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6114782691001892},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5345498919487},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.49013790488243103},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.48755425214767456},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.48615214228630066},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.47292736172676086},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.43037763237953186},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35166671872138977},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10590323805809021}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8706473112106323},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7364498376846313},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6114782691001892},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5345498919487},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.49013790488243103},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.48755425214767456},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.48615214228630066},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.47292736172676086},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.43037763237953186},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35166671872138977},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10590323805809021},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130941493","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130941493","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1505546553","https://openalex.org/W1557931734","https://openalex.org/W1586663846","https://openalex.org/W1981355037","https://openalex.org/W1993798057","https://openalex.org/W1999413555","https://openalex.org/W2019651381","https://openalex.org/W2019794334","https://openalex.org/W2020150158","https://openalex.org/W2033474604","https://openalex.org/W2033511209","https://openalex.org/W2038158348","https://openalex.org/W2052059821","https://openalex.org/W2064650029","https://openalex.org/W2070409288","https://openalex.org/W2072822417","https://openalex.org/W2075706482","https://openalex.org/W2075979998","https://openalex.org/W2085440994","https://openalex.org/W2092527476","https://openalex.org/W2094211749","https://openalex.org/W2124244274","https://openalex.org/W4244061773"],"related_works":["https://openalex.org/W2367641551","https://openalex.org/W2010057865","https://openalex.org/W3040162855","https://openalex.org/W2481151534","https://openalex.org/W2363028408","https://openalex.org/W3212473031","https://openalex.org/W2392736212","https://openalex.org/W4287747751","https://openalex.org/W2063036314","https://openalex.org/W2364060407"],"abstract_inverted_index":{"For":[0],"an":[1],"indexed":[2],"collection":[3],"of":[4,15,18,64],"convex":[5],"sets":[6],"in":[7],"a":[8],"Banach":[9],"space":[10],"with":[11,53],"index":[12],"set":[13],"$I$":[14],"cardinality":[16],"$|I|$":[17,101],"$I$,":[19],"which":[20],"may":[21],"be":[22,103],"finite":[23,92],"or":[24],"infinite,":[25],"we":[26,59],"investigate":[27],"the":[28,35,38,41,61,91,95],"interrelationship":[29],"between":[30],"various":[31],"qualification":[32],"notions":[33],"including":[34],"linear":[36],"regularity,":[37],"normal":[39,43],"property,":[40,47],"dual":[42],"conical":[44],"hull":[45],"intersection":[46],"and":[48,57,67,77,80],"Jameson's":[49],"property":[50],"$(G)$,":[51],"together":[52],"their":[54],"quantitative":[55],"versions,":[56],"thereby":[58],"extend":[60],"well-known":[62],"results":[63],"Bakan,":[65],"Deutsch,":[66],"Li":[68,81],"[Trans.":[69],"Amer.":[70],"Math.":[71],"Soc.,":[72],"357":[73],"(2005),":[74],"pp.":[75,88],"3831--3863],":[76],"Bauschke,":[78],"Borwein,":[79],"[Math.":[82],"Program.":[83],"Ser.":[84],"A,":[85],"86":[86],"(1999),":[87],"135--160]":[89],"from":[90],"case":[93,98],"to":[94,102],"more":[96],"general":[97],"that":[99],"allows":[100],"infinite.":[104]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
