{"id":"https://openalex.org/W2002371412","doi":"https://doi.org/10.1137/090766413","title":"Second-Order Analysis of Polyhedral Systems in Finite and Infinite Dimensions with Applications to Robust Stability of Variational Inequalities","display_name":"Second-Order Analysis of Polyhedral Systems in Finite and Infinite Dimensions with Applications to Robust Stability of Variational Inequalities","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2002371412","doi":"https://doi.org/10.1137/090766413","mag":"2002371412"},"language":"en","primary_location":{"id":"doi:10.1137/090766413","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090766413","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/A5111442239","display_name":"Ren\u00e9 Henrion","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ren\u00e9 Henrion","raw_affiliation_strings":["henrion@wias-berlin.de#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"henrion@wias-berlin.de#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066241737","display_name":"Boris S. Mordukhovich","orcid":"https://orcid.org/0000-0002-6071-6049"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Boris S. Mordukhovich","raw_affiliation_strings":["boris@math.wayne.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"boris@math.wayne.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002094273","display_name":"Nguyen Mau Nam","orcid":"https://orcid.org/0000-0003-4850-2301"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nguyen Mau Nam","raw_affiliation_strings":["nguyenmn@utpa.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"nguyenmn@utpa.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.6758,"has_fulltext":false,"cited_by_count":82,"citation_normalized_percentile":{"value":0.97035992,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"20","issue":"5","first_page":"2199","last_page":"2227"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9962000250816345,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9884999990463257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8530741930007935},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.8029047250747681},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.7285431027412415},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6091170907020569},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.5518829226493835},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5187031030654907},{"id":"https://openalex.org/keywords/variational-analysis","display_name":"Variational analysis","score":0.5084623098373413},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4870593845844269},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46156802773475647},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46036210656166077},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4570465683937073},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4343893527984619},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.416671484708786},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38046061992645264},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32826125621795654},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32679176330566406},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.15869596600532532},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1305347979068756},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12794229388237},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10456934571266174}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8530741930007935},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.8029047250747681},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7285431027412415},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6091170907020569},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.5518829226493835},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5187031030654907},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.5084623098373413},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4870593845844269},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46156802773475647},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46036210656166077},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4570465683937073},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4343893527984619},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.416671484708786},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38046061992645264},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32826125621795654},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32679176330566406},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.15869596600532532},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1305347979068756},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12794229388237},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10456934571266174},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/090766413","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090766413","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:digitalcommons.wayne.edu:math_reports-1063","is_oa":false,"landing_page_url":"https://digitalcommons.wayne.edu/math_reports/64","pdf_url":null,"source":{"id":"https://openalex.org/S171990522","display_name":"Human Biology","issn_l":"0018-7143","issn":["0018-7143","1534-6617"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310316469","host_organization_name":"Wayne State University Press","host_organization_lineage":["https://openalex.org/P4310316469"],"host_organization_lineage_names":["Wayne State University Press"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Research Reports","raw_type":"tech_report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.841.3241","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.841.3241","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article%3D1063%26context%3Dmath_reports","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W21204387","https://openalex.org/W345014192","https://openalex.org/W580326200","https://openalex.org/W1543439990","https://openalex.org/W1608145022","https://openalex.org/W1967737508","https://openalex.org/W1991203806","https://openalex.org/W1993647205","https://openalex.org/W1996975947","https://openalex.org/W2010337082","https://openalex.org/W2022853838","https://openalex.org/W2034902472","https://openalex.org/W2068025262","https://openalex.org/W2073311565","https://openalex.org/W2084699486","https://openalex.org/W2086592650","https://openalex.org/W2093266057","https://openalex.org/W2142789187","https://openalex.org/W2146187364","https://openalex.org/W2153149049","https://openalex.org/W2153562582","https://openalex.org/W2166234392","https://openalex.org/W3157341860","https://openalex.org/W4248907873","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2093863472","https://openalex.org/W2142789187","https://openalex.org/W1561544985","https://openalex.org/W1992673508","https://openalex.org/W2116234265","https://openalex.org/W2075980626","https://openalex.org/W36023795","https://openalex.org/W2037516588","https://openalex.org/W256114436","https://openalex.org/W4249083923"],"abstract_inverted_index":{"This":[0,93],"paper":[1,69,145],"concerns":[2],"second-order":[3,99],"analysis":[4,53,101],"for":[5,21,64,112,153],"a":[6,50],"remarkable":[7],"class":[8],"of":[9,24,33,59,76,86,98,116,128,139,162],"variational":[10,39,100,121],"systems":[11],"in":[12,89,104,143,150,158,167],"finite-dimensional":[13],"and":[14,26,45,109,137],"infinite-dimensional":[15,159],"spaces,":[16],"which":[17],"is":[18],"particularly":[19],"important":[20],"the":[22,60,73,77,83,95,125,129,147,151,154],"study":[23],"optimization":[25],"equilibrium":[27,30],"problems":[28,155],"with":[29,123],"constraints.":[31],"Systems":[32],"this":[34,68,144],"type":[35],"are":[36,146,164],"described":[37],"via":[38,82],"inequalities":[40,122],"over":[41],"polyhedral":[42,87],"convex":[43],"sets":[44,88],"allow":[46],"us":[47],"to":[48,106,119],"provide":[49],"comprehensive":[51],"local":[52],"by":[54],"using":[55],"appropriate":[56],"generalized":[57],"differentiation":[58],"normal":[61,78],"cone":[62,79],"mappings":[63,80],"such":[65],"sets.":[66],"In":[67],"we":[70],"efficiently":[71],"compute":[72],"required":[74],"coderivatives":[75],"exclusively":[81],"initial":[84],"data":[85],"reflexive":[90],"Banach":[91],"spaces.":[92,160],"provides":[94],"main":[96],"tools":[97],"allowing":[102],"us,":[103],"particular,":[105],"derive":[107],"necessary":[108],"sufficient":[110],"conditions":[111],"robust":[113,140],"Lipschitzian":[114,131],"stability":[115,141],"solution":[117],"maps":[118],"parameterized":[120],"evaluating":[124],"exact":[126],"bound":[127],"corresponding":[130],"moduli.":[132],"The":[133],"efficient":[134],"coderivative":[135],"calculations":[136],"characterizations":[138],"obtained":[142],"first":[148],"results":[149],"literature":[152],"under":[156],"consideration":[157],"Most":[161],"them":[163],"also":[165],"new":[166],"finite":[168],"dimensions.":[169]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-18T07:39:51.176621","created_date":"2025-10-10T00:00:00"}
