{"id":"https://openalex.org/W2048100837","doi":"https://doi.org/10.1137/120876915","title":"An Euler--Newton Continuation Method for Tracking Solution Trajectories of Parametric Variational Inequalities","display_name":"An Euler--Newton Continuation Method for Tracking Solution Trajectories of Parametric Variational Inequalities","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2048100837","doi":"https://doi.org/10.1137/120876915","mag":"2048100837"},"language":"en","primary_location":{"id":"doi:10.1137/120876915","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120876915","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/A5083269925","display_name":"Asen L. Dontchev","orcid":"https://orcid.org/0000-0003-3160-7828"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"A. L. Dontchev","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062048570","display_name":"Mikhail Krastanov","orcid":"https://orcid.org/0000-0001-5343-7087"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"M. I. Krastanov","raw_affiliation_strings":["Vienna University of Technology"],"affiliations":[{"raw_affiliation_string":"Vienna University of Technology","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046903273","display_name":"R. T. Rockafellar","orcid":"https://orcid.org/0000-0003-1703-5069"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. T. Rockafellar","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5026250785","display_name":"Vladimir M. Veliov","orcid":"https://orcid.org/0000-0001-6737-1250"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. M. Veliov","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5083269925"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9588,"has_fulltext":false,"cited_by_count":65,"citation_normalized_percentile":{"value":0.90916856,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"51","issue":"3","first_page":"1823","last_page":"1840"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9980000257492065,"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":0.9980000257492065,"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":0.9965999722480774,"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/T10848","display_name":"Advanced Multi-Objective Optimization Algorithms","score":0.9921000003814697,"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":0.8915930986404419},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7455320954322815},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.6671915054321289},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.5450577735900879},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.5278655886650085},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.518997311592102},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4884907007217407},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.43241891264915466},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.431222528219223},{"id":"https://openalex.org/keywords/h\u00f6lder-condition","display_name":"H\u00f6lder condition","score":0.4300786256790161},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.4208759665489197},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.41587385535240173},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2299647331237793},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17428767681121826}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8915930986404419},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7455320954322815},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.6671915054321289},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.5450577735900879},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.5278655886650085},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.518997311592102},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4884907007217407},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.43241891264915466},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.431222528219223},{"id":"https://openalex.org/C553313952","wikidata":"https://www.wikidata.org/wiki/Q1537963","display_name":"H\u00f6lder condition","level":2,"score":0.4300786256790161},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.4208759665489197},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.41587385535240173},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2299647331237793},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17428767681121826},{"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/120876915","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120876915","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:CiteSeerX.psu:10.1.1.298.9874","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.9874","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.washington.edu/~rtr/papers/rtr-TrackingVI.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.432.1963","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.432.1963","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.washington.edu/~rtr/papers/rtr-TrackingVI.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1968679317","https://openalex.org/W1993647205","https://openalex.org/W2012167011","https://openalex.org/W2016599513","https://openalex.org/W2047018462","https://openalex.org/W2060894416","https://openalex.org/W2061157561","https://openalex.org/W2071800913","https://openalex.org/W2088986191","https://openalex.org/W2109783572","https://openalex.org/W2186590998","https://openalex.org/W2496276084","https://openalex.org/W2783442388","https://openalex.org/W4236449688"],"related_works":["https://openalex.org/W2156359122","https://openalex.org/W4221091651","https://openalex.org/W4243706127","https://openalex.org/W2758222473","https://openalex.org/W2802818731","https://openalex.org/W2043536252","https://openalex.org/W2745450580","https://openalex.org/W3160070104","https://openalex.org/W2099438388","https://openalex.org/W65006171"],"abstract_inverted_index":{"A":[0],"finite-dimensional":[1],"variational":[2],"inequality":[3],"parameterized":[4],"by":[5],"$t\\in":[6],"[0,1]$":[7],"is":[8,25,32,67,82,103,135],"studied":[9],"under":[10],"the":[11,17,57,59,64,68,71,77,87,130],"assumption":[12],"that":[13,34,52],"each":[14,49,54],"point":[15,27],"of":[16,19,28,56,61,63,70,73,79,111,124],"graph":[18],"its":[20],"generally":[21],"set-valued":[22],"solution":[23,65,101],"mapping":[24,66],"a":[26,100,116],"strongly":[29],"regularity.":[30],"It":[31],"shown":[33],"there":[35],"are":[36],"finitely":[37],"many":[38],"Lipschitz":[39],"continuous":[40],"functions":[41],"on":[42],"$[0,1]$":[43],"whose":[44],"graphs":[45],"do":[46],"not":[47],"intersect":[48],"other":[50],"such":[51,91],"for":[53,98,120],"value":[55],"parameter":[58,88],"set":[60],"values":[62,72],"union":[69],"these":[74],"functions.":[75],"Moreover,":[76],"property":[78],"strong":[80],"regularity":[81],"uniform":[83],"with":[84],"respect":[85],"to":[86,107],"along":[89],"any":[90],"function":[92],"graph.":[93],"An":[94],"Euler--Newton":[95],"continuation":[96],"method":[97],"tracking":[99,125],"trajectory":[102],"introduced":[104],"and":[105],"demonstrated":[106],"have":[108],"$l^\\infty$":[109],"accuracy":[110],"order":[112],"$O(h^4)$,":[113],"thus":[114],"generalizing":[115],"known":[117],"error":[118],"estimate":[119],"equations.":[121],"Two":[122],"examples":[123],"economic":[126],"equilibrium":[127],"parametrically":[128],"illustrate":[129],"theoretical":[131],"results.":[132],"(A":[133],"correction":[134],"attached.)":[136]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
