{"id":"https://openalex.org/W2155312546","doi":"https://doi.org/10.1137/120875223","title":"Convergence of Regularized Time-Stepping Methods for Differential Variational Inequalities","display_name":"Convergence of Regularized Time-Stepping Methods for Differential Variational Inequalities","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2155312546","doi":"https://doi.org/10.1137/120875223","mag":"2155312546"},"language":"en","primary_location":{"id":"doi:10.1137/120875223","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120875223","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":true,"oa_status":"green","oa_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/7013/1/Chen_Convergence_Regularized_Time-stepping.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100369445","display_name":"Xiaojun Chen","orcid":"https://orcid.org/0000-0002-6627-2637"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Xiaojun Chen","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100348315","display_name":"Zhengyu Wang","orcid":"https://orcid.org/0000-0003-0681-2299"},"institutions":[{"id":"https://openalex.org/I881766915","display_name":"Nanjing University","ror":"https://ror.org/01rxvg760","country_code":"CN","type":"education","lineage":["https://openalex.org/I881766915"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengyu Wang","raw_affiliation_strings":["Department of Mathematics, Nanjing University, Nanjing, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Nanjing University, Nanjing, People's Republic of China","institution_ids":["https://openalex.org/I881766915"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100369445"],"corresponding_institution_ids":["https://openalex.org/I14243506"],"apc_list":null,"apc_paid":null,"fwci":2.9589,"has_fulltext":true,"cited_by_count":64,"citation_normalized_percentile":{"value":0.91379038,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":"3","first_page":"1647","last_page":"1671"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9995999932289124,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9995999932289124,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9990000128746033,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.806374192237854},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6831493377685547},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5901429653167725},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5878878831863403},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.5200352668762207},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.5081655979156494},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4921087622642517},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.47093477845191956},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4489986002445221},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.42964670062065125},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41544532775878906},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32179439067840576},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.25203025341033936},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.16651186347007751}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.806374192237854},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6831493377685547},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5901429653167725},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5878878831863403},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.5200352668762207},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.5081655979156494},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4921087622642517},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.47093477845191956},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4489986002445221},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.42964670062065125},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41544532775878906},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32179439067840576},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.25203025341033936},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.16651186347007751},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120875223","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120875223","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:ira.lib.polyu.edu.hk:10397/7013","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/7013","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/7013/1/Chen_Convergence_Regularized_Time-stepping.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal/Magazine Article"}],"best_oa_location":{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/7013","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/7013","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/7013/1/Chen_Convergence_Regularized_Time-stepping.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal/Magazine Article"},"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G2376276132","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G2664573543","display_name":null,"funder_award_id":"11302030","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4147536781","display_name":null,"funder_award_id":"1302030","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5200009302","display_name":null,"funder_award_id":"1113020301","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5853068400","display_name":null,"funder_award_id":"10871092","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322598","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2155312546.pdf","grobid_xml":"https://content.openalex.org/works/W2155312546.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W161478465","https://openalex.org/W656727543","https://openalex.org/W1507925093","https://openalex.org/W1518854728","https://openalex.org/W1543439990","https://openalex.org/W1551360398","https://openalex.org/W2000151369","https://openalex.org/W2006593825","https://openalex.org/W2018753153","https://openalex.org/W2021418814","https://openalex.org/W2038038281","https://openalex.org/W2038303744","https://openalex.org/W2042160447","https://openalex.org/W2072477022","https://openalex.org/W2075825252","https://openalex.org/W2081880850","https://openalex.org/W2094263082","https://openalex.org/W2098982596","https://openalex.org/W2109783572","https://openalex.org/W2113593360","https://openalex.org/W2116410318","https://openalex.org/W2149675356","https://openalex.org/W2160928060","https://openalex.org/W2161859543","https://openalex.org/W2169337538","https://openalex.org/W2333916009","https://openalex.org/W2585176903","https://openalex.org/W2593063709"],"related_works":["https://openalex.org/W2085771669","https://openalex.org/W2415812220","https://openalex.org/W2383497899","https://openalex.org/W1580058299","https://openalex.org/W3134869168","https://openalex.org/W4239916020","https://openalex.org/W2144455869","https://openalex.org/W2562269091","https://openalex.org/W1992673508","https://openalex.org/W2000701071"],"abstract_inverted_index":{"This":[0,139],"paper":[1,140],"provides":[2],"convergence":[3,170,190],"analysis":[4],"of":[5,17,20,42,85,93,109,112,162,171,180],"regularized":[6,164,173],"time-stepping":[7,44,95,165,174],"methods":[8],"for":[9,55,97],"the":[10,31,57,78,94,98,105,110,113,121,142,147,153,163,169,172,181,189],"differential":[11,22],"variational":[12,27],"inequality":[13,28],"(DVI),":[14],"which":[15,150],"consists":[16],"a":[18,25,43,134,156,177],"system":[19,102],"ordinary":[21],"equations":[23],"and":[24,46,67,103,107,126,183],"parametric":[26,86],"(PVI)":[29],"as":[30],"constraint.":[32],"The":[33],"PVI":[34,122,154],"often":[35],"has":[36,155],"multiple":[37],"solutions":[38],"at":[39,90,159],"each":[40,91,160],"step":[41,92,161],"method,":[45],"it":[47],"is":[48,123,130,137],"hard":[49],"to":[50,81,146,176,187],"choose":[51],"an":[52],"appropriate":[53],"solution":[54,128,136,158,179],"guaranteeing":[56],"convergence.":[58],"In":[59],"[L.":[60],"Han,":[61],"A.":[62],"Tiwari,":[63],"M.":[64],"K.":[65],"Camlibel":[66],"J.-S.":[68],"Pang,":[69],"SIAM":[70],"J.":[71],"Numer.":[72],"Anal.,":[73],"47":[74],"(2009)":[75],"pp.":[76],"3768--3796],":[77],"authors":[79],"proposed":[80],"use":[82,111],"\u201cleast-norm":[83],"solutions\u201d":[84],"linear":[87,100],"complementarity":[88,101],"problems":[89],"method":[96,175],"monotone":[99,125],"showed":[104],"novelty":[106],"advantages":[108],"least-norm":[114,135],"solutions.":[115],"However,":[116],"in":[117],"numerical":[118,185],"implementation,":[119],"when":[120],"not":[124,131],"its":[127],"set":[129],"convex,":[132],"finding":[133],"difficult.":[138],"extends":[141],"Tikhonov":[143],"regularization":[144],"approximation":[145],"P$_0$-function":[148],"DVI,":[149],"ensures":[151],"that":[152],"unique":[157],"method.":[166],"We":[167],"show":[168],"weak":[178],"DVI":[182],"present":[184],"examples":[186],"illustrate":[188],"theorems.":[191]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
