{"id":"https://openalex.org/W2018843371","doi":"https://doi.org/10.1137/s0363012900372477","title":"Existence and Limiting Behavior of a Non--Interior-Point Trajectory for Nonlinear Complementarity Problems Without Strict Feasibility Condition","display_name":"Existence and Limiting Behavior of a Non--Interior-Point Trajectory for Nonlinear Complementarity Problems Without Strict Feasibility Condition","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2018843371","doi":"https://doi.org/10.1137/s0363012900372477","mag":"2018843371"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012900372477","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012900372477","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/A5050493484","display_name":"Yun-Bin Zhao","orcid":"https://orcid.org/0000-0001-9285-2793"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yun-Bin Zhao","raw_affiliation_strings":["Chinese University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100745907","display_name":"Duan Li","orcid":"https://orcid.org/0000-0001-9786-6238"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Duan Li","raw_affiliation_strings":["Chinese University of Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Chinese University of Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":null,"apc_paid":null,"fwci":1.7035,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.82182628,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"40","issue":"3","first_page":"898","last_page":"924"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9861000180244446,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9861000180244446,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.977400004863739,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9754999876022339,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8463863730430603},{"id":"https://openalex.org/keywords/nonlinear-complementarity-problem","display_name":"Nonlinear complementarity problem","score":0.6412655115127563},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.6228180527687073},{"id":"https://openalex.org/keywords/complementarity","display_name":"Complementarity (molecular biology)","score":0.6064401865005493},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.5877931118011475},{"id":"https://openalex.org/keywords/mixed-complementarity-problem","display_name":"Mixed complementarity problem","score":0.5239161252975464},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5050130486488342},{"id":"https://openalex.org/keywords/linear-complementarity-problem","display_name":"Linear complementarity problem","score":0.49857664108276367},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4784160256385803},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.4737955927848816},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4689190983772278},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.4687129855155945},{"id":"https://openalex.org/keywords/complementarity-theory","display_name":"Complementarity theory","score":0.45560896396636963},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4369012117385864},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.43643343448638916},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42897939682006836},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.424233078956604},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42136138677597046},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12553611397743225},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09741950035095215}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8463863730430603},{"id":"https://openalex.org/C2778646529","wikidata":"https://www.wikidata.org/wiki/Q16948724","display_name":"Nonlinear complementarity problem","level":4,"score":0.6412655115127563},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.6228180527687073},{"id":"https://openalex.org/C202269582","wikidata":"https://www.wikidata.org/wiki/Q2644277","display_name":"Complementarity (molecular biology)","level":2,"score":0.6064401865005493},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.5877931118011475},{"id":"https://openalex.org/C77196050","wikidata":"https://www.wikidata.org/wiki/Q6883962","display_name":"Mixed complementarity problem","level":3,"score":0.5239161252975464},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5050130486488342},{"id":"https://openalex.org/C34320192","wikidata":"https://www.wikidata.org/wiki/Q783105","display_name":"Linear complementarity problem","level":3,"score":0.49857664108276367},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4784160256385803},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.4737955927848816},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4689190983772278},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.4687129855155945},{"id":"https://openalex.org/C85404239","wikidata":"https://www.wikidata.org/wiki/Q5156417","display_name":"Complementarity theory","level":3,"score":0.45560896396636963},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4369012117385864},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.43643343448638916},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42897939682006836},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.424233078956604},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42136138677597046},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12553611397743225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09741950035095215},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0363012900372477","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012900372477","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:10.1.1.604.4541","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.604.4541","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://web.mat.bham.ac.uk/Y.Zhao/My publication/sicon.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/a3c96180-e27e-4b60-9b66-78c07bcbbbc5","is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/a3c96180-e27e-4b60-9b66-78c07bcbbbc5","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Li, D & Zhao, Y-B 2001, 'Exixtence and limiting behaviour of a non-interior point trajectory for nonlinear complementarity problems without strict feasibility condition', SIAM Journal on Control and Optimisation, vol. 40, no. 3, pp. 898-924. https://doi.org/10.1137/S0363012900372477","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.4699999988079071,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W85094843","https://openalex.org/W184596359","https://openalex.org/W291192329","https://openalex.org/W1504470592","https://openalex.org/W1511829901","https://openalex.org/W1537108755","https://openalex.org/W1538102214","https://openalex.org/W1544526981","https://openalex.org/W1553507387","https://openalex.org/W1553741403","https://openalex.org/W1570961610","https://openalex.org/W1970000960","https://openalex.org/W1981229337","https://openalex.org/W1985538244","https://openalex.org/W2000151369","https://openalex.org/W2008814958","https://openalex.org/W2012726395","https://openalex.org/W2015957593","https://openalex.org/W2016273776","https://openalex.org/W2024670401","https://openalex.org/W2030169236","https://openalex.org/W2033711900","https://openalex.org/W2038505155","https://openalex.org/W2044382581","https://openalex.org/W2051269616","https://openalex.org/W2059352176","https://openalex.org/W2061027379","https://openalex.org/W2065691568","https://openalex.org/W2067254478","https://openalex.org/W2076622878","https://openalex.org/W2090694590","https://openalex.org/W2093246563","https://openalex.org/W2108105954","https://openalex.org/W2117634766","https://openalex.org/W2138947309","https://openalex.org/W2149675356","https://openalex.org/W2185657671","https://openalex.org/W4247607990","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2091810828","https://openalex.org/W2761564338","https://openalex.org/W2097564522","https://openalex.org/W4312668273","https://openalex.org/W2767061585","https://openalex.org/W2126747412","https://openalex.org/W2963018695","https://openalex.org/W2050897335","https://openalex.org/W2038257044","https://openalex.org/W2044498705"],"abstract_inverted_index":{"For":[0],"P":[1,20,74,120],"0":[2,75],"-complementarity":[3,22,76],"problems,":[4],"most":[5,89],"existing":[6],"non--interior-point":[7,59,71,129],"path-following":[8],"methods":[9],"require":[10],"the":[11,24,34,37,40,67,93,108,127,139,147,158],"existence":[12,25,65],"of":[13,26,39,69,98,149],"a":[14,19,27,48,57,81,119,142],"strictly":[15,28],"feasible":[16,29],"point.":[17],"(For":[18],"*":[21,121],"problem,":[23],"point":[30,156],"is":[31,62,86,101,133],"equivalent":[32],"to":[33,114],"nonemptyness":[35],"and":[36,66,132,136,152],"boundedness":[38,68],"solution":[41],"set.)":[42],"In":[43,116],"this":[44,70,99,150],"paper,":[45],"we":[46],"propose":[47],"new":[49,58,128],"homotopy":[50],"formulation":[51],"for":[52,73,118],"complementarity":[53],"problems":[54,77],"by":[55],"which":[56],"continuation":[60],"trajectory":[61,72,130,151],"generated.":[63],"The":[64],"are":[78],"proved":[79],"under":[80],"very":[82],"mild":[83],"condition":[84,100,112],"that":[85,102,126],"weaker":[87],"than":[88],"conditions":[90],"used":[91],"in":[92],"literature.":[94],"One":[95],"prominent":[96],"feature":[97],"it":[103,123],"may":[104],"hold":[105],"even":[106],"when":[107],"often-assumed":[109],"strict":[110],"feasibility":[111],"fails":[113],"hold.":[115],"particular,":[117],"-problem":[122],"turns":[124],"out":[125],"exists":[131],"bounded":[134],"if":[135,138],"only":[137],"problem":[140],"has":[141],"solution.":[143],"We":[144],"also":[145],"study":[146],"convergence":[148],"characterize":[153],"its":[154],"limiting":[155],"as":[157],"parameter":[159],"approaches":[160],"zero.":[161]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
