{"id":"https://openalex.org/W3170692334","doi":"https://doi.org/10.1007/s10107-022-01820-9","title":"Analysis of the Frank\u2013Wolfe method for convex composite optimization involving a logarithmically-homogeneous barrier","display_name":"Analysis of the Frank\u2013Wolfe method for convex composite optimization involving a logarithmically-homogeneous barrier","publication_year":2022,"publication_date":"2022-05-14","ids":{"openalex":"https://openalex.org/W3170692334","doi":"https://doi.org/10.1007/s10107-022-01820-9","mag":"3170692334"},"language":"lv","primary_location":{"id":"doi:10.1007/s10107-022-01820-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-022-01820-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01820-9.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01820-9.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002868460","display_name":"Renbo Zhao","orcid":"https://orcid.org/0000-0002-8226-9243"},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Renbo Zhao","raw_affiliation_strings":["MIT Operations Research Center, 77 Massachusetts Avenue, Cambridge, MA, 02139, UK"],"raw_orcid":"https://orcid.org/0000-0002-8226-9243","affiliations":[{"raw_affiliation_string":"MIT Operations Research Center, 77 Massachusetts Avenue, Cambridge, MA, 02139, UK","institution_ids":["https://openalex.org/I4210110987"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101429270","display_name":"Robert M. Freund","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert M. Freund","raw_affiliation_strings":["MIT Sloan School of Management, 77 Massachusetts Avenue, Cambridge, MA, 02139, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MIT Sloan School of Management, 77 Massachusetts Avenue, Cambridge, MA, 02139, UK","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002868460"],"corresponding_institution_ids":["https://openalex.org/I4210110987"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2190,"currency":"EUR","value_usd":2890},"fwci":3.8428,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.93506494,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"199","issue":"1-2","first_page":"123","last_page":"163"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9991999864578247,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5362213850021362},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2518458664417267}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5362213850021362},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2518458664417267}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10107-022-01820-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-022-01820-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01820-9.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/142541","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/142541","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Springer Berlin Heidelberg","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"doi:10.1007/s10107-022-01820-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10107-022-01820-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10107-022-01820-9.pdf","source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7965013243","display_name":null,"funder_award_id":"FA9550-19-1-0240","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3170692334.pdf","grobid_xml":"https://content.openalex.org/works/W3170692334.grobid-xml"},"referenced_works_count":66,"referenced_works":["https://openalex.org/W905619","https://openalex.org/W187211397","https://openalex.org/W597610935","https://openalex.org/W605736217","https://openalex.org/W1632601927","https://openalex.org/W1967662298","https://openalex.org/W2003146967","https://openalex.org/W2004304255","https://openalex.org/W2009144907","https://openalex.org/W2012819062","https://openalex.org/W2013243898","https://openalex.org/W2014116058","https://openalex.org/W2018493294","https://openalex.org/W2020111712","https://openalex.org/W2030161963","https://openalex.org/W2039472483","https://openalex.org/W2040676043","https://openalex.org/W2050892949","https://openalex.org/W2064868327","https://openalex.org/W2069629287","https://openalex.org/W2076095618","https://openalex.org/W2078735805","https://openalex.org/W2082366275","https://openalex.org/W2097970385","https://openalex.org/W2103559027","https://openalex.org/W2103589000","https://openalex.org/W2105864171","https://openalex.org/W2112980792","https://openalex.org/W2124541940","https://openalex.org/W2132488568","https://openalex.org/W2136885855","https://openalex.org/W2138663260","https://openalex.org/W2139182243","https://openalex.org/W2140180727","https://openalex.org/W2144578442","https://openalex.org/W2154057697","https://openalex.org/W2158713176","https://openalex.org/W2165323796","https://openalex.org/W2264518955","https://openalex.org/W2296319761","https://openalex.org/W2482485328","https://openalex.org/W2490794238","https://openalex.org/W2501216490","https://openalex.org/W2535496140","https://openalex.org/W2551153860","https://openalex.org/W2584865002","https://openalex.org/W2621075174","https://openalex.org/W2625685405","https://openalex.org/W2949979136","https://openalex.org/W2963306789","https://openalex.org/W2963663060","https://openalex.org/W2964177174","https://openalex.org/W2996588099","https://openalex.org/W3001429770","https://openalex.org/W3006200496","https://openalex.org/W3009614481","https://openalex.org/W3033834807","https://openalex.org/W3035571955","https://openalex.org/W3099983917","https://openalex.org/W3103871524","https://openalex.org/W3106237033","https://openalex.org/W3141595720","https://openalex.org/W3178749228","https://openalex.org/W3217162660","https://openalex.org/W4250589301","https://openalex.org/W6600076646"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2317200988","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2947381795"],"abstract_inverted_index":{"Abstract":[0],"We":[1,60,163],"present":[2,224],"and":[3,48,103,129,174,217,246],"analyze":[4],"a":[5,32,45,53],"new":[6,179],"generalized":[7,64,235],"Frank\u2013Wolfe":[8,65,131,158,236],"method":[9,66,159,180,188,206,237],"for":[10,202],"the":[11,49,99,108,130,136,144,157,166,191,203,208,211,230],"composite":[12],"optimization":[13],"problem":[14,169,250],"$$(P):":[15],"{\\min":[16],"}_{x\\in":[17],"{\\mathbb":[18],"{R}}^n}":[19],"\\;":[20],"f(\\mathsf":[21],"{A}":[22],"x)":[23],"+":[24,70,72,76,78],"h(x)$$":[25],"<mml:math":[26,35,42,81,89,96,105,124],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>P</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>:</mml:mo><mml:msub><mml:mo>min</mml:mo><mml:mrow><mml:mi>x</mml:mi><mml:mo>\u2208</mml:mo><mml:msup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mi>n</mml:mi></mml:msup></mml:mrow></mml:msub><mml:mspace/><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>A</mml:mi><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>":[27],",":[28],"where":[29,93],"f":[30],"is":[31,44,57,107,181,215],"$$\\theta":[33,122],"$$":[34,88,123],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03b8</mml:mi></mml:math>":[36,125],"-logarithmically-homogeneous":[37],"self-concordant":[38],"barrier,":[39],"$$\\mathsf":[40],"{A}$$":[41],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>A</mml:mi></mml:math>":[43],"linear":[46],"operator":[47],"function":[50,214],"h":[51,111],"has":[52,218],"bounded":[54],"domain":[55],"but":[56],"possibly":[58],"non-smooth.":[59],"show":[61,176],"that":[62,177,210,227],"our":[63,178,234],"requires":[67],"$$O((\\delta":[68],"_0":[69],"\\theta":[71],"R_h)\\ln":[73],"(\\delta":[74],"_0)":[75],"(\\theta":[77],"R_h)^2/\\varepsilon":[79],")$$":[80],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>\u03b4</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:mi>\u03b8</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>ln</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>\u03b4</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>\u03b8</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mi>R</mml:mi><mml:mi>h</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup><mml:mo>/</mml:mo><mml:mi>\u03b5</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>":[82],"iterations":[83],"to":[84,135,183,190,197,229],"produce":[85],"an":[86,184],"$$\\varepsilon":[87],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>\u03b5</mml:mi></mml:math>":[90],"-approximate":[91],"solution,":[92],"$$\\delta":[94],"_0$$":[95],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>\u03b4</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>":[97],"denotes":[98],"initial":[100],"optimality":[101],"gap":[102],"$$R_h$$":[104],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:msub><mml:mi>R</mml:mi><mml:mi>h</mml:mi></mml:msub></mml:math>":[106],"variation":[109],"of":[110,170,233],"on":[112,238,247],"its":[113],"domain.":[114,220],"This":[115,194],"result":[116],"establishes":[117],"certain":[118],"intrinsic":[119],"connections":[120],"between":[121],"-logarithmically":[126],"homogeneous":[127],"barriers":[128],"method.":[132],"When":[133],"specialized":[134],"D":[137],"-optimal":[138],"design":[139],"problem,":[140],"we":[141,175,223],"essentially":[142],"recover":[143],"complexity":[145,200],"obtained":[146],"by":[147],"Khachiyan":[148],"(Math":[149],"Oper":[150],"Res":[151],"21":[152],"(2):":[153],"307\u2013320,":[154],"1996)":[155],"using":[156],"with":[160,243],"exact":[161],"line-search.":[162],"also":[164],"study":[165],"(Fenchel)":[167],"dual":[168,192,212],"(":[171],"P":[172],"),":[173],"equivalent":[182],"adaptive-step-size":[185],"mirror":[186,204],"descent":[187,205],"applied":[189],"problem.":[193],"enables":[195],"us":[196],"provide":[198],"iteration":[199],"bounds":[201],"despite":[207],"fact":[209],"objective":[213],"non-Lipschitz":[216],"unbounded":[219],"In":[221],"addition,":[222],"computational":[225],"experiments":[226],"point":[228],"potential":[231],"usefulness":[232],"Poisson":[239],"image":[240],"de-blurring":[241],"problems":[242],"TV":[244],"regularization,":[245],"simulated":[248],"PET":[249],"instances.":[251]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
