{"id":"https://openalex.org/W2071100567","doi":"https://doi.org/10.1137/s1052623496300015","title":"Global Linear and Local Quadratic Convergence of a Long-Step Adaptive-Mode Interior Point Method for Some Monotone Variational Inequality Problems","display_name":"Global Linear and Local Quadratic Convergence of a Long-Step Adaptive-Mode Interior Point Method for Some Monotone Variational Inequality Problems","publication_year":1998,"publication_date":"1998-02-01","ids":{"openalex":"https://openalex.org/W2071100567","doi":"https://doi.org/10.1137/s1052623496300015","mag":"2071100567"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623496300015","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623496300015","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/A5100618850","display_name":"Jie Sun","orcid":"https://orcid.org/0000-0001-5611-1672"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jie Sun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111436924","display_name":"Gongyun Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gongyun Zhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1039,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.92074039,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"8","issue":"1","first_page":"123","last_page":"139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9987999796867371,"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":0.9987999796867371,"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":0.9940000176429749,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9929999709129333,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.871291995048523},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.7784490585327148},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.670900821685791},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6232360005378723},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6125090718269348},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.6010185480117798},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5501344203948975},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.53094482421875},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.5200031399726868},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.4585528075695038},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44675326347351074},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4117787480354309},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3869837820529938},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30857062339782715},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.24342072010040283},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.20996534824371338},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07822158932685852},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0609951913356781}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.871291995048523},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7784490585327148},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.670900821685791},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6232360005378723},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6125090718269348},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.6010185480117798},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5501344203948975},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.53094482421875},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.5200031399726868},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.4585528075695038},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44675326347351074},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4117787480354309},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3869837820529938},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30857062339782715},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.24342072010040283},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.20996534824371338},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07822158932685852},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0609951913356781},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1052623496300015","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623496300015","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:scholarbank.nus.edu.sg:10635/45072","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/45072","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W46053003","https://openalex.org/W67212155","https://openalex.org/W189973867","https://openalex.org/W1965504435","https://openalex.org/W1966090303","https://openalex.org/W1967307266","https://openalex.org/W1976750320","https://openalex.org/W1992241390","https://openalex.org/W2009303151","https://openalex.org/W2014885585","https://openalex.org/W2016598776","https://openalex.org/W2019302444","https://openalex.org/W2050897335","https://openalex.org/W2051192977","https://openalex.org/W2061027379","https://openalex.org/W2094161173","https://openalex.org/W2094359668","https://openalex.org/W4239974430","https://openalex.org/W4240941193"],"related_works":["https://openalex.org/W2037790839","https://openalex.org/W2085771669","https://openalex.org/W2383497899","https://openalex.org/W2083575507","https://openalex.org/W2026496434","https://openalex.org/W1533868172","https://openalex.org/W2382148394","https://openalex.org/W2224859476","https://openalex.org/W37717830","https://openalex.org/W2344593339"],"abstract_inverted_index":{"An":[0],"interior":[1,28],"point":[2],"(IP)":[3],"method":[4,19],"is":[5,56,65],"proposed":[6],"to":[7,42,77,81],"solve":[8],"variational":[9],"inequality":[10],"problems":[11],"for":[12],"monotone":[13],"functions":[14],"and":[15],"polyhedral":[16],"sets.":[17],"The":[18,48,68],"has":[20],"the":[21,35,53,83],"following":[22],"advantages:":[23],"1.":[24],"Given":[25],"an":[26,44],"initial":[27],"feasible":[29],"solution":[30],"with":[31],"duality":[32,54],"gap":[33,55],"$\\mu_0$,":[34],"algorithm":[36,69],"requires":[37],"at":[38],"most":[39],"$O[n\\log(\\mu_0/\\ep)]$":[40],"iterations":[41],"obtain":[43],"ep-optimal":[45],"solution.":[46],"2.":[47],"rate":[49],"of":[50,52],"convergence":[51],"q-quadratic.":[57],"3.":[58],"At":[59],"each":[60],"iteration,":[61],"a":[62,74,78],"long-step":[63],"improvement":[64],"allowed.":[66],"4.":[67],"can":[70],"automatically":[71],"transfer":[72],"from":[73],"linear":[75],"mode":[76,80],"quadratic":[79],"accelerate":[82],"local":[84],"convergence.":[85]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
