{"id":"https://openalex.org/W2017132046","doi":"https://doi.org/10.1137/s0363012996298990","title":"Lipschitz-Type Stability in Nonsmooth Convex Programs","display_name":"Lipschitz-Type Stability in Nonsmooth Convex Programs","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2017132046","doi":"https://doi.org/10.1137/s0363012996298990","mag":"2017132046"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012996298990","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012996298990","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and 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/A5011531611","display_name":"Robert Janin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert Janin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5073759268","display_name":"Jacques Gauvin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jacques Gauvin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9696,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.74797867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"38","issue":"1","first_page":"124","last_page":"137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9988999962806702,"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":0.9861999750137329,"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":0.8984864950180054},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8353258371353149},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5904679298400879},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5668279528617859},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5563826560974121},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5130261778831482},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5125088691711426},{"id":"https://openalex.org/keywords/linear-matrix-inequality","display_name":"Linear matrix inequality","score":0.501171350479126},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4776500463485718},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47471535205841064},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46742600202560425},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4400528073310852},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.43932634592056274},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.4191990792751312},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3459511399269104},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32475805282592773},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06683233380317688},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.052497535943984985}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8984864950180054},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8353258371353149},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5904679298400879},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5668279528617859},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5563826560974121},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5130261778831482},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5125088691711426},{"id":"https://openalex.org/C201829737","wikidata":"https://www.wikidata.org/wiki/Q2022760","display_name":"Linear matrix inequality","level":2,"score":0.501171350479126},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4776500463485718},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47471535205841064},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46742600202560425},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4400528073310852},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.43932634592056274},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.4191990792751312},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3459511399269104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32475805282592773},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06683233380317688},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.052497535943984985},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/s0363012996298990","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012996298990","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:publications.polymtl.ca:28884","is_oa":false,"landing_page_url":"https://publications.polymtl.ca/28884/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401013","display_name":"PolyPublie (\u00c9cole Polytechnique de Montr\u00e9al)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45683168","host_organization_name":"Polytechnique Montr\u00e9al","host_organization_lineage":["https://openalex.org/I45683168"],"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":"Article de revue"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5699999928474426}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1553702074","https://openalex.org/W1967784957","https://openalex.org/W1969331293","https://openalex.org/W1993647205","https://openalex.org/W2014746566","https://openalex.org/W2018508199","https://openalex.org/W2019256091","https://openalex.org/W2027378843","https://openalex.org/W2036613704","https://openalex.org/W2066483531","https://openalex.org/W2067863345","https://openalex.org/W2097287227","https://openalex.org/W2136273765","https://openalex.org/W2145559986","https://openalex.org/W2218983664","https://openalex.org/W2297199636","https://openalex.org/W2403650548"],"related_works":["https://openalex.org/W2072255091","https://openalex.org/W2761731838","https://openalex.org/W2007576447","https://openalex.org/W2084754442","https://openalex.org/W2043733263","https://openalex.org/W2137493863","https://openalex.org/W2356261519","https://openalex.org/W2379359887","https://openalex.org/W2185500298","https://openalex.org/W3199288759"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,15,22],"upper":[4,44],"Lipschitzian":[5,45],"continuity":[6,46],"of":[7,42],"the":[8,33,40,43],"optimal":[9],"solution":[10],"to":[11],"parametrized":[12],"convex":[13,24],"programs":[14],"linear":[16],"equality":[17],"and":[18,21],"inequality":[19],"constraints":[20],"a":[23],"nondifferentiable":[25],"objective":[26,34],"function.":[27],"Under":[28],"quadratic":[29],"growth":[30],"conditions":[31],"for":[32,39],"function,":[35],"some":[36],"accurate":[37],"bound":[38],"rate":[41],"is":[47],"provided.":[48]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}