{"id":"https://openalex.org/W2632133090","doi":"https://doi.org/10.1137/16m1086741","title":"Stable Minimizers of $\\varphi$-Regular Functions","display_name":"Stable Minimizers of $\\varphi$-Regular Functions","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2632133090","doi":"https://doi.org/10.1137/16m1086741","mag":"2632133090"},"language":"en","primary_location":{"id":"doi:10.1137/16m1086741","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1086741","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/A5101743548","display_name":"Jen-Chih Yao","orcid":"https://orcid.org/0000-0002-0855-4097"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jen-Chih Yao","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","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":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5012548383","display_name":"Jiangxing Zhu","orcid":"https://orcid.org/0000-0003-4915-1793"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiangxing Zhu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101743548"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8567,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71046754,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"27","issue":"2","first_page":"1150","last_page":"1170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9990000128746033,"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"}},"topics":[{"id":"https://openalex.org/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9983000159263611,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.945900022983551,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9048088192939758},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.6858347654342651},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.6250057220458984},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5984079837799072},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5878587365150452},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49433302879333496},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45617955923080444},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4340868890285492},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3549794554710388},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3518841862678528},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17357200384140015},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.10931479930877686}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9048088192939758},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.6858347654342651},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.6250057220458984},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5984079837799072},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5878587365150452},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49433302879333496},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45617955923080444},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4340868890285492},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3549794554710388},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3518841862678528},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17357200384140015},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.10931479930877686},{"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/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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1086741","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1086741","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:ira.lib.polyu.edu.hk:10397/76549","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/76549","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G719989113","display_name":null,"funder_award_id":"11371312","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1511503348","https://openalex.org/W1578740429","https://openalex.org/W1845221925","https://openalex.org/W1967456776","https://openalex.org/W1978161240","https://openalex.org/W1984538196","https://openalex.org/W1994089414","https://openalex.org/W1996975947","https://openalex.org/W2016104348","https://openalex.org/W2024619334","https://openalex.org/W2034492412","https://openalex.org/W2043126746","https://openalex.org/W2048303135","https://openalex.org/W2054109143","https://openalex.org/W2076513259","https://openalex.org/W2286345376","https://openalex.org/W2962678300"],"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/W2950257891","https://openalex.org/W2950608639"],"abstract_inverted_index":{"In":[0],"this":[1,58],"paper,":[2],"given":[3],"an":[4],"admissible":[5],"function":[6,21,43],"$\\varphi$,":[7],"we":[8],"consider":[9],"$\\varphi$-regularity":[10],"and":[11,27,44,61],"find":[12],"it":[13],"to":[14,22],"be":[15],"a":[16,20,41],"suitable":[17],"qualification":[18],"for":[19],"satisfy":[23],"the":[24,33,45,72],"$\\varphi$-growth":[25,29,36,38],"condition":[26,39],"uniform":[28],"condition.":[30],"We":[31],"establish":[32],"relationships":[34],"between":[35],"condition/uniform":[37],"of":[40,50],"$\\varphi$-regular":[42],"corresponding":[46],"strong":[47],"metric":[48],"subregularity/regularity":[49],"its":[51],"subdifferential":[52],"mapping.":[53],"The":[54],"results":[55],"presented":[56],"in":[57,71],"paper":[59],"improve":[60],"generalize":[62],"some":[63],"existing":[64],"ones":[65],"on":[66],"stable":[67],"second-order":[68],"local":[69],"minimizers":[70],"literature.":[73]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
