{"id":"https://openalex.org/W2592679011","doi":"https://doi.org/10.1137/11085311x","title":"An Inexact Perturbed Path-Following Method for Lagrangian Decomposition in Large-Scale Separable Convex Optimization","display_name":"An Inexact Perturbed Path-Following Method for Lagrangian Decomposition in Large-Scale Separable Convex Optimization","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2592679011","doi":"https://doi.org/10.1137/11085311x","mag":"2592679011"},"language":"en","primary_location":{"id":"doi:10.1137/11085311x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11085311x","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/A5003185205","display_name":"Quoc Tran Dinh","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Quoc Tran Dinh","raw_affiliation_strings":["Statistics and Operations Research"],"affiliations":[{"raw_affiliation_string":"Statistics and Operations Research","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019114471","display_name":"Ion Necoara","orcid":"https://orcid.org/0000-0003-1102-2654"},"institutions":[{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Ion Necoara","raw_affiliation_strings":["University \u2018Politehnica\u2019 of Bucharest"],"affiliations":[{"raw_affiliation_string":"University \u2018Politehnica\u2019 of Bucharest","institution_ids":["https://openalex.org/I61641377"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014044297","display_name":"Carlo Savorgnan","orcid":null},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Carlo Savorgnan","raw_affiliation_strings":["KU Leuven"],"affiliations":[{"raw_affiliation_string":"KU Leuven","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057375078","display_name":"Moritz Diehl","orcid":"https://orcid.org/0000-0001-6556-8252"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Moritz Diehl","raw_affiliation_strings":["KU Leuven"],"affiliations":[{"raw_affiliation_string":"KU Leuven","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5003185205"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.0525,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.97525649,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":"1","first_page":"95","last_page":"125"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9993000030517578,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9977999925613403,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.8635414838790894},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7340415120124817},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.6619156002998352},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5649190545082092},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5617114305496216},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.46869397163391113},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4685457944869995},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4579857587814331},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.44329115748405457},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.43625307083129883},{"id":"https://openalex.org/keywords/frank\u2013wolfe-algorithm","display_name":"Frank\u2013Wolfe algorithm","score":0.42287302017211914},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4181441366672516},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3959214985370636},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39026227593421936},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3448251485824585},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18018034100532532},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.09968584775924683}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8635414838790894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7340415120124817},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.6619156002998352},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5649190545082092},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5617114305496216},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.46869397163391113},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4685457944869995},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4579857587814331},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.44329115748405457},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.43625307083129883},{"id":"https://openalex.org/C122268817","wikidata":"https://www.wikidata.org/wiki/Q2020318","display_name":"Frank\u2013Wolfe algorithm","level":5,"score":0.42287302017211914},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4181441366672516},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3959214985370636},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39026227593421936},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3448251485824585},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18018034100532532},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.09968584775924683},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/11085311x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/11085311x","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:lirias2repo.kuleuven.be:123456789/361656","is_oa":false,"landing_page_url":"https://lirias.kuleuven.be/bitstream/123456789/361656/3/CP_12-181.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, vol. 23 (1), Art.No. 1, (95-125)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1299685211","display_name":"Hierarchical and Distributed Model Predictive Control of Large-Scale Systems","funder_award_id":"223854","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G1747445222","display_name":null,"funder_award_id":"IUAP P6/04","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G2201698639","display_name":null,"funder_award_id":"G.0588.09","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G2425542961","display_name":null,"funder_award_id":"IUAP P6/04","funder_id":"https://openalex.org/F4320321454","funder_display_name":"Belgian Federal Science Policy Office"},{"id":"https://openalex.org/G2507322060","display_name":null,"funder_award_id":"STREP","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3007518541","display_name":null,"funder_award_id":"G.0499.04","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G3287131444","display_name":null,"funder_award_id":"G.0211.05","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G3486877242","display_name":null,"funder_award_id":"248940","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3795546119","display_name":null,"funder_award_id":"G.0558.08","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G3873045418","display_name":null,"funder_award_id":"G.0588.09","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4407856540","display_name":null,"funder_award_id":"IWT: PhD","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G5744732752","display_name":null,"funder_award_id":"G.0226.06","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G5899396625","display_name":null,"funder_award_id":"G.0320.08","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G7870244128","display_name":null,"funder_award_id":"DYSCO","funder_id":"https://openalex.org/F4320321454","funder_display_name":"Belgian Federal Science Policy Office"},{"id":"https://openalex.org/G7993048059","display_name":null,"funder_award_id":"G.0302.07","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G8269176613","display_name":null,"funder_award_id":"G.0452.04","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"},{"id":"https://openalex.org/G891549126","display_name":null,"funder_award_id":"IUAP P6/04","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G991180673","display_name":null,"funder_award_id":"G.0321.06","funder_id":"https://openalex.org/F4320327336","funder_display_name":"Vlaamse regering"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320876","display_name":"Helmholtz-Gemeinschaft","ror":"https://ror.org/0281dp749"},{"id":"https://openalex.org/F4320321454","display_name":"Belgian Federal Science Policy Office","ror":"https://ror.org/01fapfv42"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320323983","display_name":"Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii","ror":"https://ror.org/01q7jq182"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null},{"id":"https://openalex.org/F4320338388","display_name":"Eurostars","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1936682102","https://openalex.org/W1981530345","https://openalex.org/W1991482609","https://openalex.org/W2003492573","https://openalex.org/W2050705002","https://openalex.org/W2053757987","https://openalex.org/W2053764342","https://openalex.org/W2055102530","https://openalex.org/W2079261074","https://openalex.org/W2106821132","https://openalex.org/W2122205547","https://openalex.org/W2131538180","https://openalex.org/W2131869695","https://openalex.org/W2146818753","https://openalex.org/W2149454052","https://openalex.org/W2165275149","https://openalex.org/W2167732364"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W1996936972","https://openalex.org/W4283017538","https://openalex.org/W1545275724","https://openalex.org/W4387870386","https://openalex.org/W2187449906","https://openalex.org/W3011190762","https://openalex.org/W2962818859","https://openalex.org/W4310673862"],"abstract_inverted_index":{"This":[0,42],"paper":[1],"studies":[2],"an":[3,45,61,110],"inexact":[4,62,85],"perturbed":[5,63],"path-following":[6,112],"algorithm":[7,64,74,97,114],"in":[8,27],"the":[9,23,28,33,48,52,56,69,84,89,96,101],"framework":[10],"of":[11,47,55,76,83,88,95],"Lagrangian":[12],"dual":[13,58,71,91],"decomposition":[14,113],"for":[15],"solving":[16,32],"large-scale":[17],"separable":[18],"convex":[19],"programming":[20],"problems.":[21],"Unlike":[22],"exact":[24,111],"versions":[25],"considered":[26],"literature,":[29],"we":[30],"propose":[31],"primal":[34],"subproblems":[35],"inexactly":[36],"up":[37],"to":[38,44,67],"a":[39,107],"given":[40],"accuracy.":[41],"leads":[43],"inexactness":[46],"gradient":[49],"vector":[50],"and":[51,79,100,117,127],"Hessian":[53],"matrix":[54],"smoothed":[57,70,90],"function.":[59,72],"Then":[60],"is":[65,98,104,115,121],"applied":[66],"minimize":[68],"The":[73,93],"consists":[75],"two":[77],"phases,":[78],"both":[80],"make":[81],"use":[82],"derivative":[86],"information":[87],"problem.":[92],"convergence":[94],"analyzed,":[99],"worst-case":[102,119],"complexity":[103,120],"estimated.":[105],"As":[106],"special":[108],"case,":[109],"obtained":[116],"its":[118],"given.":[122],"Implementation":[123],"details":[124],"are":[125,131],"discussed,":[126],"preliminary":[128],"numerical":[129],"results":[130],"reported.":[132]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
