{"id":"https://openalex.org/W2082155814","doi":"https://doi.org/10.1137/060659132","title":"Linear Regularity for a Collection of Subsmooth Sets in Banach Spaces","display_name":"Linear Regularity for a Collection of Subsmooth Sets in Banach Spaces","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2082155814","doi":"https://doi.org/10.1137/060659132","mag":"2082155814"},"language":"en","primary_location":{"id":"doi:10.1137/060659132","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060659132","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/A5056391377","display_name":"Xi Yin Zheng","orcid":"https://orcid.org/0000-0002-5314-6471"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Xi Yin Zheng","raw_affiliation_strings":["xyzheng@ynu.edu.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"xyzheng@ynu.edu.cn#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014862456","display_name":"Kung Fu Ng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kung Fu Ng","raw_affiliation_strings":["kfng@math.cuhk.edu.hk#TAB#"],"affiliations":[{"raw_affiliation_string":"kfng@math.cuhk.edu.hk#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056391377"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5275,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.94449503,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"1","first_page":"62","last_page":"76"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/mathematics","display_name":"Mathematics","score":0.8974879384040833},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.7468484044075012},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6151072382926941},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5779969692230225},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4980194568634033},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42521312832832336},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3674790859222412},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06162962317466736},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.05366906523704529}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8974879384040833},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.7468484044075012},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6151072382926941},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5779969692230225},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4980194568634033},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42521312832832336},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3674790859222412},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06162962317466736},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05366906523704529},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/060659132","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060659132","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.162.3183","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.162.3183","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cuhk.edu.hk/~kfng/Zheng_Ng_Subsmooth.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1492700492","https://openalex.org/W1505546553","https://openalex.org/W1551360398","https://openalex.org/W1573659356","https://openalex.org/W1586663846","https://openalex.org/W1601960826","https://openalex.org/W1877455765","https://openalex.org/W1967505494","https://openalex.org/W1993798057","https://openalex.org/W1994089414","https://openalex.org/W1999413555","https://openalex.org/W2033474604","https://openalex.org/W2033511209","https://openalex.org/W2036159573","https://openalex.org/W2038998663","https://openalex.org/W2048303135","https://openalex.org/W2064650029","https://openalex.org/W2075706482","https://openalex.org/W2082451773","https://openalex.org/W2094211749","https://openalex.org/W2145867192","https://openalex.org/W2153562582","https://openalex.org/W2246422272","https://openalex.org/W2396132789","https://openalex.org/W2955198501","https://openalex.org/W4240533965","https://openalex.org/W4242192912"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W2278466645","https://openalex.org/W2323683917","https://openalex.org/W2006145505","https://openalex.org/W1033935582","https://openalex.org/W2350748817","https://openalex.org/W2013897026","https://openalex.org/W2008268341","https://openalex.org/W2409258641","https://openalex.org/W4386644491"],"abstract_inverted_index":{"Using":[0],"variational":[1],"analysis,":[2],"we":[3,18],"study":[4],"the":[5,23,36,41,52],"linear":[6,24,43],"regularity":[7,25,44],"for":[8,26],"a":[9,27],"collection":[10,28],"of":[11,22,29],"finitely":[12,30],"many":[13,31],"closed":[14,32],"sets.":[15],"In":[16],"particular,":[17],"extend":[19],"duality":[20],"characterizations":[21],"convex":[33],"sets":[34],"to":[35],"possibly":[37],"nonconvex":[38],"setting.":[39],"Moreover,":[40],"sharpest":[42],"constant":[45],"can":[46],"also":[47],"be":[48],"dually":[49],"represented":[50],"under":[51],"subsmoothness":[53],"assumption.":[54]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}