{"id":"https://openalex.org/W2619280982","doi":"https://doi.org/10.1137/17m1130794","title":"Characterization of Tilt Stability via Subgradient Graphical Derivative with Applications to Nonlinear Programming","display_name":"Characterization of Tilt Stability via Subgradient Graphical Derivative with Applications to Nonlinear Programming","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2619280982","doi":"https://doi.org/10.1137/17m1130794","mag":"2619280982"},"language":"en","primary_location":{"id":"doi:10.1137/17m1130794","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1130794","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1705.09745","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026663625","display_name":"Nguy\u1ec5n Huy Chi\u00eau","orcid":"https://orcid.org/0000-0003-3492-3156"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nguyen Huy Chieu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064063674","display_name":"Le Van Hien","orcid":"https://orcid.org/0000-0003-1787-3011"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Le Van Hien","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5075913105","display_name":"T. T. A. Nghia","orcid":"https://orcid.org/0000-0001-7016-6450"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tran T. A. Nghia","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5026663625"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2137,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51351048,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"28","issue":"3","first_page":"2246","last_page":"2273"},"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":0.9987000226974487,"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":0.9642999768257141,"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/subgradient-method","display_name":"Subgradient method","score":0.8498604893684387},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.6696245670318604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6625285148620605},{"id":"https://openalex.org/keywords/tilt","display_name":"Tilt (camera)","score":0.5736569166183472},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5721027851104736},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5480809211730957},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.5326052904129028},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.521776020526886},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.47499051690101624},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.4740217328071594},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4685426950454712},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36422377824783325},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22167038917541504},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19513863325119019},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13077181577682495}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.8498604893684387},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.6696245670318604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6625285148620605},{"id":"https://openalex.org/C2779844322","wikidata":"https://www.wikidata.org/wiki/Q2919140","display_name":"Tilt (camera)","level":2,"score":0.5736569166183472},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5721027851104736},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5480809211730957},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.5326052904129028},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.521776020526886},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.47499051690101624},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.4740217328071594},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4685426950454712},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36422377824783325},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22167038917541504},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19513863325119019},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13077181577682495},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/17m1130794","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1130794","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:arXiv.org:1705.09745","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.09745","pdf_url":"https://arxiv.org/pdf/1705.09745","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2619280982","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1705.09745.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1705.09745","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1705.09745","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1705.09745","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.09745","pdf_url":"https://arxiv.org/pdf/1705.09745","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2530301331","display_name":null,"funder_award_id":"101.01-2017.325","funder_id":"https://openalex.org/F4320309617","funder_display_name":"National Foundation for Science and Technology Development"}],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2619280982.pdf","grobid_xml":"https://content.openalex.org/works/W2619280982.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1511503348","https://openalex.org/W1518440404","https://openalex.org/W1567995217","https://openalex.org/W1601741115","https://openalex.org/W1608145022","https://openalex.org/W1965287024","https://openalex.org/W1973879592","https://openalex.org/W1978161240","https://openalex.org/W1991359458","https://openalex.org/W1993647205","https://openalex.org/W1996975947","https://openalex.org/W2014715559","https://openalex.org/W2022853838","https://openalex.org/W2034492412","https://openalex.org/W2042401377","https://openalex.org/W2043126746","https://openalex.org/W2044615981","https://openalex.org/W2046537588","https://openalex.org/W2048843365","https://openalex.org/W2069612911","https://openalex.org/W2069691851","https://openalex.org/W2083231020","https://openalex.org/W2086194488","https://openalex.org/W2094214271","https://openalex.org/W2106156434","https://openalex.org/W2128672267","https://openalex.org/W2150140216","https://openalex.org/W2169604001","https://openalex.org/W2189118132","https://openalex.org/W2285572974","https://openalex.org/W2525178759","https://openalex.org/W2553174903","https://openalex.org/W2588676540","https://openalex.org/W2962678300","https://openalex.org/W2963313014","https://openalex.org/W3157341860"],"related_works":["https://openalex.org/W2147810192","https://openalex.org/W3170874782","https://openalex.org/W3172629593","https://openalex.org/W2129181728","https://openalex.org/W1556421578","https://openalex.org/W21456002","https://openalex.org/W2189462150","https://openalex.org/W2275788826","https://openalex.org/W1978804995","https://openalex.org/W1971230463","https://openalex.org/W2092412812","https://openalex.org/W2027741643","https://openalex.org/W2094234047","https://openalex.org/W1986384742","https://openalex.org/W2012579815","https://openalex.org/W2247931801","https://openalex.org/W2758953509","https://openalex.org/W2606421266","https://openalex.org/W2017276091","https://openalex.org/W2041037772"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,104],"devoted":[3],"to":[4,64],"the":[5,15,19,47,52,56,68,99,110],"study":[6],"of":[7,17,28,36,42,46,51,93],"tilt":[8,83],"stability":[9],"in":[10,40,58],"finite":[11],"dimensional":[12],"optimization":[13,38],"via":[14],"approach":[16],"using":[18],"subgradient":[20,48],"graphical":[21,49],"derivative.":[22],"We":[23],"establish":[24],"a":[25,33,43,94,105],"new":[26,79],"characterization":[27],"tilt-stable":[29,106],"local":[30,107],"minimizers":[31],"for":[32,82],"broad":[34],"class":[35],"unconstrained":[37],"problems":[39],"terms":[41],"uniform":[44],"positive-definiteness":[45],"derivative":[50],"objective":[53],"function":[54],"around":[55],"point":[57,92],"question.":[59],"By":[60],"applying":[61],"this":[62],"result":[63],"nonlinear":[65,95],"programming":[66,96],"under":[67],"metric":[69,100],"subregularity":[70,101],"constraint":[71,102],"qualification,":[72],"we":[73,87],"derive":[74],"second-order":[75,113],"characterizations":[76],"and":[77],"several":[78],"sufficient":[80,114],"conditions":[81],"stability.":[84],"In":[85],"particular,":[86],"show":[88],"that":[89],"each":[90],"stationary":[91],"problem":[97],"satisfying":[98],"qualification":[103],"minimizer":[108],"if":[109],"classical":[111],"strong":[112],"condition":[115],"holds.":[116]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}