{"id":"https://openalex.org/W2022083862","doi":"https://doi.org/10.1137/s0363012998339216","title":"Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis","display_name":"Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2022083862","doi":"https://doi.org/10.1137/s0363012998339216","mag":"2022083862"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012998339216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012998339216","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/A5038275535","display_name":"Abderrahim Jourani","orcid":"https://orcid.org/0000-0002-9774-2742"},"institutions":[{"id":"https://openalex.org/I177064439","display_name":"Universit\u00e9 de Bourgogne","ror":"https://ror.org/03k1bsr36","country_code":"FR","type":"education","lineage":["https://openalex.org/I177064439"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Abderrahim Jourani","raw_affiliation_strings":["University of Burgundy ,"],"affiliations":[{"raw_affiliation_string":"University of Burgundy ,","institution_ids":["https://openalex.org/I177064439"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038275535"],"corresponding_institution_ids":["https://openalex.org/I177064439"],"apc_list":null,"apc_paid":null,"fwci":3.2791,"has_fulltext":false,"cited_by_count":79,"citation_normalized_percentile":{"value":0.91809453,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"38","issue":"3","first_page":"947","last_page":"970"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9983000159263611,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9833999872207642,"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":0.9090250730514526},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.8552066087722778},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8236094117164612},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.7208976149559021},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5904999375343323},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5772950053215027},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.48631343245506287},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48208481073379517},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.42242273688316345},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3661462962627411},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3394225239753723}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9090250730514526},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.8552066087722778},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8236094117164612},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.7208976149559021},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5904999375343323},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5772950053215027},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.48631343245506287},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48208481073379517},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.42242273688316345},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3661462962627411},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3394225239753723},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"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},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0363012998339216","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012998339216","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.699999988079071,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W177396124","https://openalex.org/W185728265","https://openalex.org/W1492700492","https://openalex.org/W1528330203","https://openalex.org/W1551360398","https://openalex.org/W1586250694","https://openalex.org/W1608145022","https://openalex.org/W1960239420","https://openalex.org/W1970396175","https://openalex.org/W1981955268","https://openalex.org/W1985842349","https://openalex.org/W1991607307","https://openalex.org/W1994433358","https://openalex.org/W2010337082","https://openalex.org/W2011461289","https://openalex.org/W2018399640","https://openalex.org/W2021305110","https://openalex.org/W2026692276","https://openalex.org/W2027698658","https://openalex.org/W2033186119","https://openalex.org/W2033604629","https://openalex.org/W2042614948","https://openalex.org/W2051943091","https://openalex.org/W2061907550","https://openalex.org/W2064114733","https://openalex.org/W2065012151","https://openalex.org/W2066932332","https://openalex.org/W2067951301","https://openalex.org/W2069369032","https://openalex.org/W2072058266","https://openalex.org/W2072344559","https://openalex.org/W2079488098","https://openalex.org/W2080674898","https://openalex.org/W2083030901","https://openalex.org/W2085563112","https://openalex.org/W2087566894","https://openalex.org/W2088302576","https://openalex.org/W2090462597","https://openalex.org/W2094503739","https://openalex.org/W2096534942","https://openalex.org/W2097287227","https://openalex.org/W2334285086","https://openalex.org/W2347049040","https://openalex.org/W2583666619","https://openalex.org/W2955198501","https://openalex.org/W4248564526","https://openalex.org/W4299815621"],"related_works":["https://openalex.org/W2036697162","https://openalex.org/W2332386680","https://openalex.org/W2561315646","https://openalex.org/W2248621902","https://openalex.org/W2003779889","https://openalex.org/W4205698120","https://openalex.org/W4239246781","https://openalex.org/W2542825942","https://openalex.org/W3201620972","https://openalex.org/W1496421768"],"abstract_inverted_index":{"Our":[0],"aim":[1],"is":[2,89],"to":[3,17,71],"present":[4],"sufficient":[5,66],"conditions":[6,67],"ensuring":[7],"Hoffman'serror":[8],"bound":[9,80,88],"for":[10,28,96],"lower":[11],"semicontinuous":[12],"nonconvex":[13],"inequality":[14,98],"systems":[15],"and":[16,36,39],"analyze":[18],"its":[19],"impact":[20],"on":[21,40],"the":[22,62,92,101],"local":[23],"controllability,":[24],"implicit":[25],"function":[26],"theorem":[27],"(non-Lipschitz)":[29],"multivalued":[30,48],"mappings,":[31],"generalized":[32],"equations":[33],"(variational":[34],"inequalities),":[35],"sensitivity":[37],"analysis":[38],"other":[41],"problems":[42],"like":[43],"Lipschitzian":[44],"properties":[45],"of":[46],"polyhedral":[47],"mappings":[49],"as":[50,52],"well":[51],"weak":[53],"sharp":[54],"minima":[55],"or":[56],"linear":[57,97],"conditioning.":[58],"We":[59,82],"show":[60,84],"how":[61],"information":[63],"about":[64],"our":[65,104],"can":[68],"be":[69,107],"used":[70],"provide":[72],"a":[73],"computable":[74],"constant":[75,105],"such":[76],"that":[77,85],"Hoffman's":[78],"error":[79,87],"holds.":[81],"also":[83],"this":[86],"nothing":[90],"but":[91],"classical":[93],"Farkas":[94],"lemma":[95],"systems.":[99],"In":[100],"latter":[102],"case":[103],"may":[106],"computed":[108],"explicitly.":[109]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}