{"id":"https://openalex.org/W1996975947","doi":"https://doi.org/10.1137/s1052623496309296","title":"Tilt Stability of a Local Minimum","display_name":"Tilt Stability of a Local Minimum","publication_year":1998,"publication_date":"1998-05-01","ids":{"openalex":"https://openalex.org/W1996975947","doi":"https://doi.org/10.1137/s1052623496309296","mag":"1996975947"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623496309296","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623496309296","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/A5109925491","display_name":"R. A. Poliquin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. A. Poliquin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5046903273","display_name":"R. T. Rockafellar","orcid":"https://orcid.org/0000-0003-1703-5069"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. T. Rockafellar","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109925491"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.0683,"has_fulltext":false,"cited_by_count":177,"citation_normalized_percentile":{"value":0.938408,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"8","issue":"2","first_page":"287","last_page":"299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9991000294685364,"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":0.9991000294685364,"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":0.9980999827384949,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9927999973297119,"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/hessian-matrix","display_name":"Hessian matrix","score":0.9265204668045044},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8663270473480225},{"id":"https://openalex.org/keywords/tilt","display_name":"Tilt (camera)","score":0.6511144638061523},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.60007643699646},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5431877374649048},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.5394613742828369},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.529351532459259},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4970097839832306},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.47448018193244934},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40546759963035583},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3547768294811249},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35148411989212036},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17682325839996338},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07181096076965332}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.9265204668045044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8663270473480225},{"id":"https://openalex.org/C2779844322","wikidata":"https://www.wikidata.org/wiki/Q2919140","display_name":"Tilt (camera)","level":2,"score":0.6511144638061523},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.60007643699646},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5431877374649048},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.5394613742828369},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.529351532459259},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4970097839832306},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.47448018193244934},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40546759963035583},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3547768294811249},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35148411989212036},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17682325839996338},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07181096076965332},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1052623496309296","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623496309296","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:10.1.1.161.8245","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.161.8245","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.washington.edu/~rtr/papers/rtr-TiltStability.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Climate action","score":0.5,"id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W34431499","https://openalex.org/W43435585","https://openalex.org/W105472411","https://openalex.org/W160520070","https://openalex.org/W1511503348","https://openalex.org/W1968363522","https://openalex.org/W1978527164","https://openalex.org/W1987589111","https://openalex.org/W2010337082","https://openalex.org/W2016456744","https://openalex.org/W2022853838","https://openalex.org/W2046144679","https://openalex.org/W2053549375","https://openalex.org/W2057361274","https://openalex.org/W2065012151","https://openalex.org/W2076627354","https://openalex.org/W2081233504","https://openalex.org/W2084673064","https://openalex.org/W2088302576","https://openalex.org/W2093020024","https://openalex.org/W2096534942","https://openalex.org/W2117500014","https://openalex.org/W2132677982","https://openalex.org/W2157170476","https://openalex.org/W2327793148","https://openalex.org/W2329275945","https://openalex.org/W2506419233","https://openalex.org/W4239970194","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W1996936972","https://openalex.org/W4283017538","https://openalex.org/W1545275724","https://openalex.org/W2802707792","https://openalex.org/W2569979269","https://openalex.org/W2075777916","https://openalex.org/W3021699548","https://openalex.org/W4291718021"],"abstract_inverted_index":{"The":[0,29],"behavior":[1],"of":[2,23,32,54],"a":[3,14,33,55,75],"minimizing":[4,70],"point":[5,71],"when":[6],"an":[7,45],"objective":[8],"function":[9],"is":[10,18,41],"tilted":[11],"by":[12],"adding":[13],"small":[15],"linear":[16],"term":[17],"studied":[19],"from":[20],"the":[21,52,63,69],"perspective":[22],"second-order":[24],"conditions":[25],"for":[26],"local":[27],"optimality.":[28],"classical":[30],"condition":[31],"positive-definite":[34],"Hessian":[35,58],"in":[36,51,74],"smooth":[37],"problems":[38],"without":[39],"constraints":[40],"found":[42],"to":[43,72],"have":[44],"exact":[46],"counterpart":[47],"much":[48],"more":[49],"broadly":[50],"positivity":[53],"certain":[56],"generalized":[57],"mapping.":[59],"This":[60],"fully":[61],"characterizes":[62],"case":[64],"where":[65],"tilt":[66],"perturbations":[67],"cause":[68],"shift":[73],"Lipschitzian":[76],"manner.":[77]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":13},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":13},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":14},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
