{"id":"https://openalex.org/W2021548137","doi":"https://doi.org/10.1137/100814494","title":"Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective","display_name":"Convergence Analysis of Primal-Dual Algorithms for a Saddle-Point Problem: From Contraction Perspective","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2021548137","doi":"https://doi.org/10.1137/100814494","mag":"2021548137"},"language":"en","primary_location":{"id":"doi:10.1137/100814494","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100814494","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","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/A5039946576","display_name":"Bingsheng He","orcid":"https://orcid.org/0000-0001-8618-4581"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bingsheng He","raw_affiliation_strings":["hebma@nju.edu.cn#TAB#"],"affiliations":[{"raw_affiliation_string":"hebma@nju.edu.cn#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060269704","display_name":"Xiaoming Yuan","orcid":"https://orcid.org/0000-0002-6900-6983"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiaoming Yuan","raw_affiliation_strings":["xmyuan@hkbu.edu.hk#TAB#"],"affiliations":[{"raw_affiliation_string":"xmyuan@hkbu.edu.hk#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039946576"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":33.5221,"has_fulltext":false,"cited_by_count":385,"citation_normalized_percentile":{"value":0.99965559,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"5","issue":"1","first_page":"119","last_page":"149"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9975000023841858,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9959999918937683,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.7690985202789307},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.7570837140083313},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.6484524011611938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6062767505645752},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5799973011016846},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5557684302330017},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5366427898406982},{"id":"https://openalex.org/keywords/contraction-mapping","display_name":"Contraction mapping","score":0.42442435026168823},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.41891929507255554},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3550657033920288},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.21505051851272583},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10883879661560059},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0699288547039032}],"concepts":[{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7690985202789307},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.7570837140083313},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.6484524011611938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6062767505645752},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5799973011016846},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5557684302330017},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5366427898406982},{"id":"https://openalex.org/C55524764","wikidata":"https://www.wikidata.org/wiki/Q515173","display_name":"Contraction mapping","level":3,"score":0.42442435026168823},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.41891929507255554},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3550657033920288},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.21505051851272583},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10883879661560059},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0699288547039032},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100814494","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100814494","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:hub.hku.hk:10722/250983","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/250983","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6100000143051147,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1970298676","https://openalex.org/W1981112674","https://openalex.org/W1985588167","https://openalex.org/W2003372231","https://openalex.org/W2016910236","https://openalex.org/W2026517977","https://openalex.org/W2038497950","https://openalex.org/W2045079045","https://openalex.org/W2061979078","https://openalex.org/W2062059813","https://openalex.org/W2092663520","https://openalex.org/W2103559027","https://openalex.org/W2118429861"],"related_works":["https://openalex.org/W2051848413","https://openalex.org/W3049220960","https://openalex.org/W2066844763","https://openalex.org/W4232554191","https://openalex.org/W3215007808","https://openalex.org/W2771077211","https://openalex.org/W2978744305","https://openalex.org/W2033071165","https://openalex.org/W4221159156","https://openalex.org/W2021548137"],"abstract_inverted_index":{"Recently,":[0],"some":[1,48],"primal-dual":[2,32,120],"algorithms":[3,33,121],"have":[4],"been":[5],"proposed":[6,60],"for":[7,61],"solving":[8,62],"a":[9],"saddle-point":[10,64,95],"problem,":[11],"with":[12,87],"particular":[13],"applications":[14],"in":[15],"the":[16,27,63,74,77,90,94,109,123,136,139],"area":[17],"of":[18,30,73,93,100,112,125,138],"total":[19],"variation":[20],"image":[21],"restoration.":[22],"This":[23],"paper":[24],"focuses":[25],"on":[26,118],"convergence":[28,99,131],"analysis":[29],"these":[31,69,82,101,119],"and":[34],"shows":[35],"that":[36,68],"their":[37],"involved":[38],"parameters":[39],"(including":[40],"step":[41],"sizes)":[42],"can":[43,105],"be":[44,106],"significantly":[45],"enlarged":[46],"if":[47],"simple":[49],"correction":[50],"steps":[51],"are":[52,58,72,85],"supplemented.":[53],"Some":[54],"new":[55,70,83,102,140],"primal-dual\u2013based":[56],"methods":[57,71,84,103,127,141],"thus":[59,104],"problem.":[65,96],"We":[66],"show":[67,135],"contraction":[75,126],"type:":[76],"iterative":[78],"sequences":[79],"generated":[80],"by":[81],"contractive":[86],"respect":[88],"to":[89],"solution":[91],"set":[92],"The":[97,115],"global":[98],"obtained":[107],"within":[108],"analytic":[110],"framework":[111],"contraction-type":[113],"methods.":[114],"novel":[116],"study":[117],"from":[122],"perspective":[124],"substantially":[128],"simplifies":[129],"existing":[130],"analysis.":[132],"Finally,":[133],"we":[134],"efficiency":[137],"numerically.":[142]},"counts_by_year":[{"year":2026,"cited_by_count":12},{"year":2025,"cited_by_count":38},{"year":2024,"cited_by_count":17},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":39},{"year":2021,"cited_by_count":37},{"year":2020,"cited_by_count":22},{"year":2019,"cited_by_count":23},{"year":2018,"cited_by_count":37},{"year":2017,"cited_by_count":22},{"year":2016,"cited_by_count":36},{"year":2015,"cited_by_count":32},{"year":2014,"cited_by_count":31},{"year":2013,"cited_by_count":13},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2016-06-24T00:00:00"}