{"id":"https://openalex.org/W1965700306","doi":"https://doi.org/10.1137/s105262349528901x","title":"Stability Theory for Linear Inequality Systems II: Upper Semicontinuity of the Solution Set Mapping","display_name":"Stability Theory for Linear Inequality Systems II: Upper Semicontinuity of the Solution Set Mapping","publication_year":1997,"publication_date":"1997-11-01","ids":{"openalex":"https://openalex.org/W1965700306","doi":"https://doi.org/10.1137/s105262349528901x","mag":"1965700306"},"language":"en","primary_location":{"id":"doi:10.1137/s105262349528901x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s105262349528901x","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/A5016160092","display_name":"Miguel \u00c1. Goberna","orcid":"https://orcid.org/0000-0002-5363-7991"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. A. Goberna","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100715600","display_name":"Marco A. L\u00f3pez","orcid":"https://orcid.org/0000-0002-0619-9618"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. A. L\u00f3pez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5010829936","display_name":"M. I. Todorov","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. I. Todorov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0732,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.85539327,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"7","issue":"4","first_page":"1138","last_page":"1151"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9987999796867371,"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":0.9987999796867371,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9890999794006348,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9240944981575012},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.6421934366226196},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.5916720628738403},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.548457145690918},{"id":"https://openalex.org/keywords/solution-set","display_name":"Solution set","score":0.49279382824897766},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.484881728887558},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4166262745857239},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4129989743232727},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3908858597278595},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3526262044906616},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33953458070755005},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.04996621608734131}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9240944981575012},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6421934366226196},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.5916720628738403},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.548457145690918},{"id":"https://openalex.org/C60033838","wikidata":"https://www.wikidata.org/wiki/Q1751685","display_name":"Solution set","level":3,"score":0.49279382824897766},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.484881728887558},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4166262745857239},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4129989743232727},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3908858597278595},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3526262044906616},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33953458070755005},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.04996621608734131},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s105262349528901x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s105262349528901x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5299999713897705,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1513869646","https://openalex.org/W1966621956","https://openalex.org/W2011451855","https://openalex.org/W2035284071","https://openalex.org/W2043962752","https://openalex.org/W2067349605","https://openalex.org/W2085515216","https://openalex.org/W2094683072","https://openalex.org/W2151135593","https://openalex.org/W3022952999"],"related_works":["https://openalex.org/W2354218792","https://openalex.org/W4288558836","https://openalex.org/W4250297294","https://openalex.org/W3200899799","https://openalex.org/W4247764056","https://openalex.org/W2081650204","https://openalex.org/W1979390716","https://openalex.org/W1993108008","https://openalex.org/W4387908483","https://openalex.org/W4281748523"],"abstract_inverted_index":{"This":[0,51],"paper":[1],"deals":[2],"with":[3,89],"the":[4,8,43,46,49,61,65,90,95,109,112,126,130],"upper":[5,127],"semicontinuity":[6,22,128],"of":[7,30,79,97,111,129],"solution":[9,139],"set":[10,44,132,140],"mapping":[11],"for":[12,125],"linear":[13,66],"inequality":[14],"systems,":[15,81],"complementing":[16],"a":[17,83,104,135],"previous":[18],"work":[19],"on":[20],"lower":[21],"and":[23,68,121],"related":[24],"stability":[25],"concepts.":[26],"The":[27,77],"main":[28],"novelty":[29],"our":[31],"approach":[32],"is":[33,87,141],"that":[34],"we":[35,117],"are":[36],"not":[37,142],"assuming":[38],"any":[39],"standard":[40],"hypothesis":[41],"about":[42],"indexing":[45],"inequalities":[47,67],"in":[48],"system.":[50],"set,":[52,86],"possibly":[53],"infinite,":[54],"has":[55,72],"no":[56,73],"topological":[57],"structure":[58],"and,":[59],"therefore,":[60],"functional":[62],"dependence":[63],"between":[64],"their":[69],"associated":[70],"indices":[71],"qualification":[74],"at":[75,134],"all.":[76],"space":[78],"consistent":[80],"over":[82],"fixed":[84],"index":[85],"endowed":[88],"uniform":[91],"topology":[92],"derived":[93],"from":[94],"pseudometric":[96],"Chebyshev,":[98],"which":[99],"turns":[100],"out":[101],"to":[102,107],"be":[103],"natural":[105],"way":[106],"measure":[108],"size":[110],"perturbations.":[113],"In":[114],"this":[115],"context,":[116],"provide":[118],"some":[119,122],"necessary":[120],"sufficient":[123],"conditions":[124],"feasible":[131],"map":[133],"given":[136],"system":[137],"whose":[138],"necessarily":[143],"bounded.":[144]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
