{"id":"https://openalex.org/W2571966084","doi":"https://doi.org/10.3233/978-1-61499-672-9-167","title":"On Stochastic Primal-Dual Hybrid Gradient Approach for Compositely Regularized Minimization","display_name":"On Stochastic Primal-Dual Hybrid Gradient Approach for Compositely Regularized Minimization","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2571966084","doi":"https://doi.org/10.3233/978-1-61499-672-9-167","mag":"2571966084"},"language":"en","primary_location":{"id":"doi:10.3233/978-1-61499-672-9-167","is_oa":true,"landing_page_url":"https://doi.org/10.3233/978-1-61499-672-9-167","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.3233/978-1-61499-672-9-167","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043045076","display_name":"Linbo Qiao","orcid":"https://orcid.org/0000-0002-8285-2738"},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qiao Linbo","raw_affiliation_strings":["College of Computer, National University of Defense Technology, Changsha, China and National Laboratory for Parallel and Distributed Processing, National University of Defense Technology, Changsha ...#TAB#"],"affiliations":[{"raw_affiliation_string":"College of Computer, National University of Defense Technology, Changsha, China and National Laboratory for Parallel and Distributed Processing, National University of Defense Technology, Changsha ...#TAB#","institution_ids":["https://openalex.org/I170215575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083720030","display_name":"Tianyi Lin","orcid":"https://orcid.org/0000-0002-5323-1852"},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin Tianyi","raw_affiliation_strings":["Research Center for Management Science and Information Analytics, Shanghai University of Finance and Economics, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Research Center for Management Science and Information Analytics, Shanghai University of Finance and Economics, Shanghai, China","institution_ids":["https://openalex.org/I181679659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047962986","display_name":"Yu\u2013Gang Jiang","orcid":"https://orcid.org/0000-0002-1907-8567"},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiang Yu-Gang","raw_affiliation_strings":[",School of Computer Science, Fudan University, Shanghai, China#TAB#"],"affiliations":[{"raw_affiliation_string":",School of Computer Science, Fudan University, Shanghai, China#TAB#","institution_ids":["https://openalex.org/I24943067"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101416578","display_name":"Fan Yang","orcid":"https://orcid.org/0000-0002-3253-3499"},"institutions":[{"id":"https://openalex.org/I181679659","display_name":"Shanghai University of Finance and Economics","ror":"https://ror.org/00wtvfq62","country_code":"CN","type":"education","lineage":["https://openalex.org/I181679659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang Fan","raw_affiliation_strings":["Research Center for Management Science and Information Analytics, Shanghai University of Finance and Economics, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Research Center for Management Science and Information Analytics, Shanghai University of Finance and Economics, Shanghai, China","institution_ids":["https://openalex.org/I181679659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100431792","display_name":"Wei Liu","orcid":"https://orcid.org/0000-0002-3865-8145"},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu Wei","raw_affiliation_strings":["Tencent AI Lab,China"],"affiliations":[{"raw_affiliation_string":"Tencent AI Lab,China","institution_ids":["https://openalex.org/I2250653659"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102809441","display_name":"Xicheng Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I170215575","display_name":"National University of Defense Technology","ror":"https://ror.org/05d2yfz11","country_code":"CN","type":"education","lineage":["https://openalex.org/I170215575"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lu Xicheng","raw_affiliation_strings":["College of Computer, National University of Defense Technology, Changsha, China and National Laboratory for Parallel and Distributed Processing, National University of Defense Technology, Changsha ...#TAB#"],"affiliations":[{"raw_affiliation_string":"College of Computer, National University of Defense Technology, Changsha, China and National Laboratory for Parallel and Distributed Processing, National University of Defense Technology, Changsha ...#TAB#","institution_ids":["https://openalex.org/I170215575"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5043045076"],"corresponding_institution_ids":["https://openalex.org/I170215575"],"apc_list":null,"apc_paid":null,"fwci":4.667,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.95575642,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"167","last_page":"174"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998000264167786,"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":0.9998000264167786,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9957000017166138,"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/dual","display_name":"Dual (grammatical number)","score":0.6934301853179932},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.6175349354743958},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5147040486335754},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4825515151023865},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4172348380088806},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35190051794052124},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.08834943175315857}],"concepts":[{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6934301853179932},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.6175349354743958},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5147040486335754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4825515151023865},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4172348380088806},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35190051794052124},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.08834943175315857},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/978-1-61499-672-9-167","is_oa":true,"landing_page_url":"https://doi.org/10.3233/978-1-61499-672-9-167","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},{"id":"mag:2571966084","is_oa":false,"landing_page_url":"http://dblp.uni-trier.de/db/conf/ecai/ecai2016.html#QiaoLJYLL16","pdf_url":null,"source":{"id":"https://openalex.org/S4306418308","display_name":"European Conference on Artificial Intelligence","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":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"European Conference on Artificial Intelligence","raw_type":null}],"best_oa_location":{"id":"doi:10.3233/978-1-61499-672-9-167","is_oa":true,"landing_page_url":"https://doi.org/10.3233/978-1-61499-672-9-167","pdf_url":null,"source":{"id":"https://openalex.org/S4210201731","display_name":"Frontiers in artificial intelligence and applications","issn_l":"0922-6389","issn":["0922-6389","1879-8314"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Artificial Intelligence and Applications","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W25321933","https://openalex.org/W38875623","https://openalex.org/W1554944419","https://openalex.org/W1563975843","https://openalex.org/W1856374787","https://openalex.org/W1948582444","https://openalex.org/W1981112674","https://openalex.org/W1993531186","https://openalex.org/W2016910236","https://openalex.org/W2021548137","https://openalex.org/W2092663520","https://openalex.org/W2096199223","https://openalex.org/W2096840748","https://openalex.org/W2148974830","https://openalex.org/W2156118598","https://openalex.org/W2510516734","https://openalex.org/W2951481254","https://openalex.org/W2952168305","https://openalex.org/W2963156201","https://openalex.org/W2963907572","https://openalex.org/W2964037929","https://openalex.org/W3047587354","https://openalex.org/W3106348863"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,17,31,76,132],"wide":[3],"spectrum":[4],"of":[5,21,33,45,66,107,119,191],"regularized":[6,26,35],"stochastic":[7],"minimization":[8],"problems,":[9],"where":[10],"the":[11,42,46,51,59,64,67,87,104,108,117,148,172],"regularization":[12,52,68],"term":[13,53,69],"is":[14,40,54,123,175],"composite":[15],"with":[16,50,137,168,179],"linear":[18,61],"function.":[19],"Examples":[20],"this":[22,94,128],"formulation":[23],"include":[24],"graph-guided":[25],"minimization,":[27],"generalized":[28],"Lasso":[29],"and":[30,159],"class":[32],"ℓ1":[34],"problems.":[36],"The":[37],"computational":[38],"challenge":[39],"that":[41,194],"closed-form":[43],"solution":[44],"proximal":[47],"mapping":[48],"associated":[49],"not":[55],"available":[56],"due":[57],"to":[58,72,177],"imposed":[60],"composition.":[62],"Fortunately,":[63],"structure":[65],"allows":[70],"us":[71],"reformulate":[73],"it":[74],"as":[75,102],"new":[77],"convex-concave":[78],"saddle":[79],"point":[80],"problem":[81],"which":[82],"can":[83],"be":[84,97,113],"solved":[85],"using":[86],"Primal-Dual":[88],"Hybrid":[89],"Gradient":[90],"(PDHG)":[91],"approach.":[92],"However,":[93],"approach":[95],"may":[96],"inefficient":[98],"in":[99,152],"realistic":[100],"applications":[101],"computing":[103],"full":[105],"gradient":[106],"expected":[109,176],"objective":[110],"function":[111],"could":[112],"very":[114],"expensive":[115],"when":[116],"number":[118],"input":[120],"data":[121],"samples":[122],"considerably":[124],"large.":[125],"To":[126],"address":[127],"issue,":[129],"we":[130],"propose":[131],"Stochastic":[133],"PDHG":[134],"(SPDHG)":[135],"algorithm":[136,150,174,197],"either":[138],"uniformly":[139,145],"or":[140],"non-uniformly":[141,169],"averaged":[142,146,170],"iterates.":[143],"Through":[144],"iterates,":[147,171],"SPDHG":[149,173],"converges":[151],"expectation":[153],"withrate":[154],"for":[155,162,182],"general":[156],"convex":[157,164,184],"objectives":[158],"O(log (t)/t)":[160],"rate":[161,181],"strongly":[163,183],"objectives,":[165],"respectively.":[166],"While":[167],"converge":[178],"O(1/t)":[180],"objectives.":[185],"Numerical":[186],"experiments":[187],"on":[188],"different":[189],"genres":[190],"datasets":[192],"demonstrate":[193],"our":[195],"proposed":[196],"outperforms":[198],"other":[199],"competing":[200],"algorithms.":[201]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}