{"id":"https://openalex.org/W4294106839","doi":"https://doi.org/10.1137/21m1420319","title":"Golden Ratio Primal-Dual Algorithm with Linesearch","display_name":"Golden Ratio Primal-Dual Algorithm with Linesearch","publication_year":2022,"publication_date":"2022-07-18","ids":{"openalex":"https://openalex.org/W4294106839","doi":"https://doi.org/10.1137/21m1420319"},"language":"en","primary_location":{"id":"doi:10.1137/21m1420319","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1420319","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/A5067886927","display_name":"Xiaokai Chang","orcid":"https://orcid.org/0000-0003-0337-2910"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiao-Kai Chang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056288677","display_name":"Junfeng Yang","orcid":"https://orcid.org/0000-0003-1981-6424"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Junfeng Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5072377630","display_name":"Hongchao Zhang","orcid":"https://orcid.org/0000-0003-2716-3267"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hongchao Zhang","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":8.2152,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.99063619,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"32","issue":"3","first_page":"1584","last_page":"1613"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"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":0.9993000030517578,"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":0.9983999729156494,"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":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8125656843185425},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5281450748443604},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5238820910453796},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.49993395805358887},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4990546703338623},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4488723576068878},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4324053227901459},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.42907586693763733},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.42285674810409546},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.33780229091644287},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33190426230430603},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13897734880447388},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.09574910998344421}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8125656843185425},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5281450748443604},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5238820910453796},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.49993395805358887},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4990546703338623},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4488723576068878},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4324053227901459},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.42907586693763733},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.42285674810409546},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.33780229091644287},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33190426230430603},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13897734880447388},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.09574910998344421},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1420319","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1420319","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3153458163","display_name":"Inexact Optimization Methods for Structured Nonlinear Optimization","funder_award_id":"1819161","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3181839671","display_name":null,"funder_award_id":"NSFC-11922111","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6007677634","display_name":"Optimization Methods for Nonconvex Structured Optimization","funder_award_id":"2110722","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7777283542","display_name":null,"funder_award_id":"21JR7RA253","funder_id":"https://openalex.org/F4320322880","funder_display_name":"Natural Science Foundation of Gansu Province"},{"id":"https://openalex.org/G8745327692","display_name":null,"funder_award_id":"NSFC-12161053","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8821156768","display_name":null,"funder_award_id":"2020YFA0713800","funder_id":"https://openalex.org/F4320321540","funder_display_name":"Ministry of Science and Technology of the People's Republic of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321540","display_name":"Ministry of Science and Technology of the People's Republic of China","ror":"https://ror.org/027s68j25"},{"id":"https://openalex.org/F4320322880","display_name":"Natural Science Foundation of Gansu Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1489128386","https://openalex.org/W1972568768","https://openalex.org/W1978259121","https://openalex.org/W1981112674","https://openalex.org/W1998991750","https://openalex.org/W2014024561","https://openalex.org/W2015292809","https://openalex.org/W2019569173","https://openalex.org/W2020123437","https://openalex.org/W2021548137","https://openalex.org/W2042650576","https://openalex.org/W2045079045","https://openalex.org/W2058532290","https://openalex.org/W2065030431","https://openalex.org/W2073932184","https://openalex.org/W2074567512","https://openalex.org/W2092663520","https://openalex.org/W2158449358","https://openalex.org/W2241435520","https://openalex.org/W2503308866","https://openalex.org/W2510358906","https://openalex.org/W2625685405","https://openalex.org/W2763081248","https://openalex.org/W2963213190","https://openalex.org/W2963353224","https://openalex.org/W2965900084","https://openalex.org/W3016074254","https://openalex.org/W3100820186","https://openalex.org/W3118876559","https://openalex.org/W3137879310","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W3202999461","https://openalex.org/W2268131559","https://openalex.org/W2400034325","https://openalex.org/W4292651679","https://openalex.org/W2499557797","https://openalex.org/W2985014567","https://openalex.org/W4299515259","https://openalex.org/W2032676126","https://openalex.org/W2187449906","https://openalex.org/W2962818859"],"abstract_inverted_index":{"The":[0,46],"golden":[1],"ratio":[2],"primal-dual":[3,55],"algorithm":[4,56],"(GRPDA)":[5],"is":[6,63,91,115,180,242,281],"a":[7,40,43,139,200,278],"new":[8],"variant":[9],"of":[10,27,30,37,58,80,89,104,111,153,223,238,270,309],"the":[11,23,28,49,53,66,101,108,112,150,154,171,216,233,239,254,267,271,290,295,307,310],"classical":[12],"Arrow--Hurwicz":[13,50],"method":[14,51],"for":[15,142,192],"solving":[16,74],"structured":[17],"convex":[18,34],"optimization":[19,226],"problems,":[20],"in":[21,65,123,132],"which":[22,38,117,144],"objective":[24],"function":[25,217],"consists":[26],"sum":[29],"two":[31],"closed":[32],"proper":[33],"functions,":[35],"one":[36,237],"involves":[39],"composition":[41],"with":[42,84],"linear":[44,78,113,155],"transform.":[45],"same":[47,255],"as":[48,199],"and":[52,60,97,161,178,184,207,220,303],"popular":[54],"(PDA)":[57],"Chambolle":[59],"Pock,":[61],"GRPDA":[62,90,105],"full-splitting":[64],"sense":[67],"that":[68,92,107,280,289],"it":[69,93,179],"does":[70,147,185],"not":[71,145,148,186],"rely":[72],"on":[73,300],"any":[75,188],"subproblems":[76],"or":[77],"system":[79],"equations":[81],"iteratively.":[82],"Compared":[83],"PDA,":[85],"an":[86,224],"important":[87,196],"feature":[88],"permits":[94],"larger":[95,164],"primal":[96],"dual":[98,172],"stepsizes.":[99,165],"However,":[100],"stepsize":[102],"condition":[103,279],"requires":[106],"spectral":[109,151],"norm":[110,152],"transform":[114,156],"known,":[116],"can":[118],"be":[119,176],"difficult":[120],"to":[121,175,294],"obtain":[122],"some":[124,262],"applications.":[125],"Furthermore,":[126],"constant":[127],"stepsizes":[128],"are":[129,228,257,274],"usually":[130],"overconservative":[131],"practice.":[133],"In":[134],"this":[135],"paper,":[136],"we":[137,287],"propose":[138],"linesearch":[140,168,312],"strategy":[141],"GRPDA,":[143],"only":[146,170],"require":[149,187],"but":[157],"also":[158],"allows":[159],"adaptive":[160],"potentially":[162],"much":[163,282],"Within":[166],"each":[167],"step,":[169],"variable":[173],"needs":[174],"updated,":[177],"thus":[181],"quite":[182],"cheap":[183],"extra":[189],"matrix-vector":[190],"multiplications":[191],"many":[193],"special":[194],"yet":[195],"applications":[197],"such":[198],"regularized":[201],"least-squares":[202],"problem.":[203],"Global":[204],"iterate":[205],"convergence":[206,211,249],"${\\cal":[208,246],"O}(1/N)$":[209],"ergodic":[210,248],"rate":[212,250],"results,":[213,251],"measured":[214],"by":[215,253,259],"value":[218],"gap":[219],"constraint":[221],"violations":[222],"equivalent":[225],"problem,":[227],"established,":[229],"where":[230],"$N$":[231],"denotes":[232],"iteration":[234],"counter.":[235],"When":[236],"component":[240,272],"functions":[241,273],"strongly":[243,275],"convex,":[244],"faster":[245],"O}(1/N^2)$":[247],"quantified":[252],"measures,":[256],"established":[258],"adaptively":[260],"choosing":[261],"algorithmic":[263],"parameters.":[264],"Moreover,":[265],"when":[266],"subdifferential":[268],"operators":[269],"metric":[276],"subregular,":[277],"weaker":[283],"than":[284],"strong":[285],"convexity,":[286],"show":[288],"iterates":[291],"converge":[292],"R-linearly":[293],"unique":[296],"solution.":[297],"Numerical":[298],"experiments":[299],"matrix":[301],"game":[302],"LASSO":[304],"problems":[305],"illustrate":[306],"effectiveness":[308],"proposed":[311],"strategy.":[313]},"counts_by_year":[{"year":2026,"cited_by_count":11},{"year":2025,"cited_by_count":17},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}