{"id":"https://openalex.org/W2024619334","doi":"https://doi.org/10.1137/140959845","title":"H\u00f6lder Stable Minimizers, Tilt Stability, and H\u00f6lder metric Regularity of Subdifferentials","display_name":"H\u00f6lder Stable Minimizers, Tilt Stability, and H\u00f6lder metric Regularity of Subdifferentials","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2024619334","doi":"https://doi.org/10.1137/140959845","mag":"2024619334"},"language":"en","primary_location":{"id":"doi:10.1137/140959845","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140959845","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":[],"affiliations":[]},{"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":[],"affiliations":[]}],"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":4.7299,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.95199247,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"25","issue":"1","first_page":"416","last_page":"438"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9990000128746033,"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":0.9990000128746033,"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":0.9901999831199646,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9842000007629395,"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/mathematics","display_name":"Mathematics","score":0.9161597490310669},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6704820394515991},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.616611659526825},{"id":"https://openalex.org/keywords/bar","display_name":"Bar (unit)","score":0.5398871302604675},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5000033378601074},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.46927013993263245},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4676384925842285},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46228504180908203},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4618825614452362},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43080809712409973},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.34081870317459106},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.27259695529937744},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.185041606426239},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.07953369617462158}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9161597490310669},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6704820394515991},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.616611659526825},{"id":"https://openalex.org/C188721877","wikidata":"https://www.wikidata.org/wiki/Q103510","display_name":"Bar (unit)","level":2,"score":0.5398871302604675},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5000033378601074},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.46927013993263245},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4676384925842285},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46228504180908203},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4618825614452362},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43080809712409973},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.34081870317459106},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.27259695529937744},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.185041606426239},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.07953369617462158},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140959845","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140959845","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":[{"display_name":"Reduced inequalities","score":0.47999998927116394,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1967015850","https://openalex.org/W1967213961","https://openalex.org/W1978161240","https://openalex.org/W1990935327","https://openalex.org/W1991093725","https://openalex.org/W1991203806","https://openalex.org/W1993962900","https://openalex.org/W1994089414","https://openalex.org/W1996975947","https://openalex.org/W2001598548","https://openalex.org/W2018775338","https://openalex.org/W2033316062","https://openalex.org/W2033474604","https://openalex.org/W2034492412","https://openalex.org/W2043126746","https://openalex.org/W2044615981","https://openalex.org/W2061360434","https://openalex.org/W2064114733","https://openalex.org/W2069691851","https://openalex.org/W2076513259","https://openalex.org/W2101730742","https://openalex.org/W2116407586","https://openalex.org/W2334285086"],"related_works":["https://openalex.org/W4296644444","https://openalex.org/W2790507665","https://openalex.org/W1966902277","https://openalex.org/W2060941687","https://openalex.org/W1993033969","https://openalex.org/W2082095722","https://openalex.org/W2067170864","https://openalex.org/W2294305148","https://openalex.org/W2549854571","https://openalex.org/W2751308593"],"abstract_inverted_index":{"Using":[0],"techniques":[1,7],"of":[2,16,49,60,75],"variational":[3],"analysis":[4],"and":[5,29,51],"dual":[6],"for":[8,12],"smooth":[9],"conjugate":[10],"functions,":[11],"a":[13,17,24,45,56],"local":[14],"minimizer":[15,48,59],"proper":[18],"lower":[19],"semicontinuous":[20],"function":[21],"$f$":[22,50],"on":[23],"Banach":[25],"space,":[26],"$p\\in":[27],"(0,\\;+\\infty)$":[28],"$q=\\frac{1+p}{p}$,":[30],"we":[31],"prove":[32],"that":[33],"the":[34,70,76],"following":[35],"two":[36],"properties":[37],"are":[38],"always":[39],"equivalent:":[40],"(i)":[41],"$\\bar":[42,53],"x$":[43,54],"is":[44,55],"stable":[46],"$q$-order":[47],"(ii)":[52],"tilt-stable":[57],"$p$-order":[58,71],"$f$.":[61],"We":[62],"also":[63],"consider":[64],"their":[65],"relationships":[66],"in":[67],"conjunction":[68],"with":[69],"strong":[72],"metric":[73],"regularity":[74],"subdifferential":[77],"mapping":[78],"$\\partial":[79],"f$.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}