{"id":"https://openalex.org/W2003341291","doi":"https://doi.org/10.1137/040607927","title":"On the Stability of the Extreme Point Set in Linear Optimization","display_name":"On the Stability of the Extreme Point Set in Linear Optimization","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2003341291","doi":"https://doi.org/10.1137/040607927","mag":"2003341291"},"language":"en","primary_location":{"id":"doi:10.1137/040607927","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607927","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":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Miguel A. Goberna","raw_affiliation_strings":["University of Alicante,"],"affiliations":[{"raw_affiliation_string":"University of Alicante,","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066718208","display_name":"Mercedes Larriqueta","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mercedes Larriqueta","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015890254","display_name":"Virginia Vera de Serio","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Virginia Vera de Serio","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5016160092"],"corresponding_institution_ids":["https://openalex.org/I130194489"],"apc_list":null,"apc_paid":null,"fwci":1.0541,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.75812927,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"4","first_page":"1155","last_page":"1169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9969000220298767,"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":0.9969000220298767,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9948999881744385,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9918000102043152,"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":0.7913188338279724},{"id":"https://openalex.org/keywords/extreme-point","display_name":"Extreme point","score":0.6452862620353699},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5850550532341003},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49816179275512695},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47745826840400696},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4484824240207672},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4377289116382599},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3791888952255249},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2664564251899719},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16046324372291565},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11636638641357422}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7913188338279724},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.6452862620353699},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5850550532341003},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49816179275512695},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47745826840400696},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4484824240207672},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4377289116382599},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3791888952255249},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2664564251899719},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16046324372291565},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11636638641357422},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040607927","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040607927","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W62594946","https://openalex.org/W83112366","https://openalex.org/W1513869646","https://openalex.org/W1606265074","https://openalex.org/W1965700306","https://openalex.org/W1967938148","https://openalex.org/W1977098977","https://openalex.org/W2011451855","https://openalex.org/W2041551615","https://openalex.org/W2045979166","https://openalex.org/W2056858424","https://openalex.org/W2111948593","https://openalex.org/W4249513058"],"related_works":["https://openalex.org/W3189643850","https://openalex.org/W2375407244","https://openalex.org/W1967774664","https://openalex.org/W2061565576","https://openalex.org/W2039994059","https://openalex.org/W2120254947","https://openalex.org/W2113698846","https://openalex.org/W111504223","https://openalex.org/W1991235662","https://openalex.org/W2915809315"],"abstract_inverted_index":{"This":[0],"paper":[1,74],"analyzes":[2],"the":[3,7,31,40,48,52,59,67,70,76,79,88,93,110,114],"stability":[4],"properties":[5,125],"of":[6,9,12,20,33,51,54,61,66,69,78,92,123],"set":[8,16,44,82,96],"extreme":[10,80,94],"points":[11],"a":[13,21],"closed":[14],"convex":[15],"described":[17],"by":[18,64],"means":[19,65],"given":[22],"linear":[23],"inequality":[24],"system":[25],"$\\sigma$.":[26,99],"We":[27],"assume":[28],"that":[29],"all":[30],"coefficients":[32],"$\\sigma$":[34,119],"can":[35],"be":[36],"arbitrarily":[37],"perturbed":[38],"maintaining":[39],"(possibly":[41],"infinite)":[42],"index":[43],"as":[45,47,104,106],"well":[46,105],"(finite)":[49],"dimension":[50],"space":[53],"variables,":[55],"and":[56,87,112],"we":[57],"measure":[58],"size":[60],"these":[62,124],"perturbations":[63,86],"pseudometric":[68],"uniform":[71],"convergence.":[72],"The":[73],"characterizes":[75],"nonemptiness":[77],"point":[81,95],"under":[83],"sufficiently":[84],"small":[85],"Berge":[89,115],"lower":[90],"semicontinuity":[91,117],"mapping":[97],"at":[98,118],"It":[100],"also":[101],"gives":[102],"necessary":[103],"sufficient":[107],"conditions":[108],"for":[109,113,126],"closedness":[111],"upper":[116],"which":[120],"provide":[121],"characterizations":[122],"finite":[127],"systems.":[128]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2013,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}