{"id":"https://openalex.org/W2125870036","doi":"https://doi.org/10.1142/s0217595915500116","title":"A Linearized Alternating Direction Method of Multipliers with Substitution Procedure","display_name":"A Linearized Alternating Direction Method of Multipliers with Substitution Procedure","publication_year":2014,"publication_date":"2014-12-21","ids":{"openalex":"https://openalex.org/W2125870036","doi":"https://doi.org/10.1142/s0217595915500116","mag":"2125870036"},"language":"en","primary_location":{"id":"doi:10.1142/s0217595915500116","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595915500116","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","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/A5048562330","display_name":"Miantao Chao","orcid":"https://orcid.org/0000-0003-4763-9533"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Miantao Chao","raw_affiliation_strings":["Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100936727","display_name":"Cao-zong Cheng","orcid":null},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Caozong Cheng","raw_affiliation_strings":["Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100356596","display_name":"Haibin Zhang","orcid":"https://orcid.org/0009-0001-1142-9289"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haibin Zhang","raw_affiliation_strings":["Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing University of Technology, Beijing 100124, P. R. China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I37796252"],"apc_list":null,"apc_paid":null,"fwci":0.3119,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.62431996,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"32","issue":"03","first_page":"1550011","last_page":"1550011"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991999864578247,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9983000159263611,"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":0.9973999857902527,"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/separable-space","display_name":"Separable space","score":0.7465935945510864},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7360073924064636},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.6562339067459106},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.6247106194496155},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5885196924209595},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5632855296134949},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5620375275611877},{"id":"https://openalex.org/keywords/substitution","display_name":"Substitution (logic)","score":0.4967721104621887},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4883372485637665},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.48604899644851685},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48276105523109436},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.4788001477718353},{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.46934211254119873},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4466243386268616},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43851161003112793},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32853472232818604},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19731968641281128},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18206492066383362},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15692728757858276}],"concepts":[{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.7465935945510864},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7360073924064636},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.6562339067459106},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.6247106194496155},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5885196924209595},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5632855296134949},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5620375275611877},{"id":"https://openalex.org/C2778220771","wikidata":"https://www.wikidata.org/wiki/Q1522579","display_name":"Substitution (logic)","level":2,"score":0.4967721104621887},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4883372485637665},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.48604899644851685},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48276105523109436},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.4788001477718353},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.46934211254119873},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4466243386268616},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43851161003112793},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32853472232818604},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19731968641281128},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18206492066383362},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15692728757858276},{"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/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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0217595915500116","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217595915500116","pdf_url":null,"source":{"id":"https://openalex.org/S1254427","display_name":"Asia Pacific Journal of Operational Research","issn_l":"0217-5959","issn":["0217-5959","1793-7019"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asia-Pacific Journal of Operational Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:apjorx:v:32:y:2015:i:03:n:s0217595915500116","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0217595915500116","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:RePEc:wsi:apjorx:v:32:y:2015:i:03:p:1550011-1-1550011-19","is_oa":false,"landing_page_url":"http://www.worldscinet.com/cgi-bin/details.cgi?type=html&id=pii:S0217595915500116","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321913","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W649579232","https://openalex.org/W1964709249","https://openalex.org/W1983357136","https://openalex.org/W1992841740","https://openalex.org/W1992910825","https://openalex.org/W1998576973","https://openalex.org/W2007822845","https://openalex.org/W2012888164","https://openalex.org/W2019569173","https://openalex.org/W2033736734","https://openalex.org/W2045079045","https://openalex.org/W2065030431","https://openalex.org/W2072536590","https://openalex.org/W2105693192","https://openalex.org/W2122712590","https://openalex.org/W2199004907","https://openalex.org/W2337718075","https://openalex.org/W2949483514","https://openalex.org/W3141222251","https://openalex.org/W4210953350","https://openalex.org/W4242750451","https://openalex.org/W4242859866","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W2155858901","https://openalex.org/W4382519099","https://openalex.org/W2491194410","https://openalex.org/W1515727993","https://openalex.org/W2037179686","https://openalex.org/W3195000156","https://openalex.org/W2112045043","https://openalex.org/W4387870386","https://openalex.org/W2187449906","https://openalex.org/W2962818859"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,34,37,44,50,73,80,88,113,116],"linearly":[3],"constrained":[4],"separable":[5,13],"convex":[6,17],"programming":[7],"problem":[8],"whose":[9],"objective":[10],"function":[11],"is":[12,56],"into":[14],"m":[15,40,53,76],"individual":[16],"functions":[18],"with":[19],"non-overlapping":[20],"variables.":[21],"The":[22],"alternating":[23],"direction":[24],"method":[25],"of":[26,47,91,115],"multipliers":[27],"(ADMM)":[28],"has":[29],"been":[30],"well":[31],"studied":[32],"in":[33,103],"literature":[35],"for":[36,49,72],"special":[38],"case":[39,52,75],"=":[41],"2,":[42],"but":[43],"direct":[45],"extension":[46],"ADMM":[48],"general":[51,74],"\u2265":[54,77],"2":[55],"not":[57],"necessarily":[58],"convergent.":[59],"In":[60],"this":[61],"paper,":[62],"we":[63,83,96],"propose":[64],"a":[65,98],"new":[66],"linearized":[67],"ADMM-based":[68],"contraction":[69],"type":[70,93],"algorithms":[71],"2.":[78],"For":[79],"proposed":[81,117],"algorithm,":[82],"prove":[84],"its":[85],"convergence":[86,101],"via":[87],"analytic":[89],"framework":[90],"contractive":[92],"methods":[94],"and":[95],"derive":[97],"worst-case":[99],"O(1/t)":[100],"rate":[102],"ergodic":[104],"sense.":[105],"Finally,":[106],"numerical":[107],"results":[108],"are":[109],"reported":[110],"to":[111],"demonstrate":[112],"effectiveness":[114],"algorithm.":[118]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}