{"id":"https://openalex.org/W4410855706","doi":"https://doi.org/10.1287/moor.2024.0580","title":"Fast Convergence of Frank-Wolfe Algorithms on Polytopes","display_name":"Fast Convergence of Frank-Wolfe Algorithms on Polytopes","publication_year":2025,"publication_date":"2025-05-29","ids":{"openalex":"https://openalex.org/W4410855706","doi":"https://doi.org/10.1287/moor.2024.0580"},"language":"en","primary_location":{"id":"doi:10.1287/moor.2024.0580","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2024.0580","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations 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/A5003837569","display_name":"Elias Wirth","orcid":"https://orcid.org/0009-0008-8957-8736"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Elias Wirth","raw_affiliation_strings":["Technical University of Berlin, 10623 Berlin, Germany"],"raw_orcid":"https://orcid.org/0009-0008-8957-8736","affiliations":[{"raw_affiliation_string":"Technical University of Berlin, 10623 Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5016340912","display_name":"Javier Pe\u00f1a","orcid":"https://orcid.org/0000-0001-5698-1918"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Javier Pe\u00f1a","raw_affiliation_strings":["Carnegie Mellon University, Pittsburgh, Pennsylvania 15213"],"raw_orcid":"https://orcid.org/0000-0001-5698-1918","affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, Pittsburgh, Pennsylvania 15213","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043574831","display_name":"Sebastian Pokutta","orcid":"https://orcid.org/0000-0001-7365-3000"},"institutions":[{"id":"https://openalex.org/I195893171","display_name":"Zuse Institute Berlin","ror":"https://ror.org/02eva5865","country_code":"DE","type":"facility","lineage":["https://openalex.org/I195893171"]},{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sebastian Pokutta","raw_affiliation_strings":["Technical University of Berlin, 10623 Berlin, Germany; and Zuse Institute Berlin, 14195 Berlin, Germany"],"raw_orcid":"https://orcid.org/0000-0001-7365-3000","affiliations":[{"raw_affiliation_string":"Technical University of Berlin, 10623 Berlin, Germany; and Zuse Institute Berlin, 14195 Berlin, Germany","institution_ids":["https://openalex.org/I195893171","https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0909,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.79959884,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"51","issue":"2","first_page":"1463","last_page":"1485"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.7882815599441528},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7525167465209961},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5974053740501404},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4804341793060303},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38107311725616455},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.344779908657074}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.7882815599441528},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7525167465209961},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5974053740501404},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4804341793060303},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38107311725616455},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.344779908657074},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1287/moor.2024.0580","is_oa":false,"landing_page_url":"https://doi.org/10.1287/moor.2024.0580","pdf_url":null,"source":{"id":"https://openalex.org/S55826652","display_name":"Mathematics of Operations Research","issn_l":"0364-765X","issn":["0364-765X","1526-5471"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315699","host_organization_name":"Institute for Operations Research and the Management Sciences","host_organization_lineage":["https://openalex.org/P4310315699"],"host_organization_lineage_names":["Institute for Operations Research and the Management Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Operations Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1963481290","https://openalex.org/W2013243898","https://openalex.org/W2028355641","https://openalex.org/W2097970385","https://openalex.org/W2129130711","https://openalex.org/W2134882453","https://openalex.org/W2135046866","https://openalex.org/W2963663060","https://openalex.org/W3023412291","https://openalex.org/W4236240466","https://openalex.org/W4387601960","https://openalex.org/W4410109211"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4280529077","https://openalex.org/W1493684871","https://openalex.org/W2886567582","https://openalex.org/W4390962314","https://openalex.org/W4289703404","https://openalex.org/W2999175164","https://openalex.org/W4387265813","https://openalex.org/W4286224459","https://openalex.org/W4320410061"],"abstract_inverted_index":{"We":[0],"provide":[1],"a":[2],"template":[3,37],"to":[4,90],"derive":[5,83],"affine-invariant":[6,46],"convergence":[7,41,86],"rates":[8,42,84],"for":[9],"the":[10,15,40,49,62,79,94,97,110,142,147],"following":[11],"popular":[12],"versions":[13],"of":[14,48,78,85,96,150],"Frank-Wolfe":[16,22,26,32],"algorithm":[17],"on":[18,61,69,93],"polytopes:":[19],"vanilla":[20],"Frank-Wolfe,":[21],"with":[23,27,33],"away":[24],"steps,":[25,30],"blended":[28],"pairwise":[29],"and":[31,54,64],"in-face":[34],"directions.":[35],"Our":[36],"shows":[38],"how":[39],"follow":[43],"from":[44,88],"two":[45],"properties":[47,58],"problem,":[50],"namely,":[51],"error":[52,98],"bound":[53],"extended":[55],"curvature.":[56],"These":[57],"depend":[59],"solely":[60],"polytope":[63],"objective":[65],"function":[66],"but":[67],"not":[68],"any":[70],"affine-dependent":[71],"object":[72],"like":[73],"norms.":[74],"For":[75],"each":[76],"one":[77],"above":[80],"algorithms,":[81],"we":[82],"ranging":[87],"sublinear":[89],"linear":[91],"depending":[92],"degree":[95],"bound.":[99],"Funding:":[100],"Research":[101,115,123,132],"reported":[102,133],"in":[103,134],"this":[104,135],"paper":[105,136],"was":[106,137],"partially":[107,139],"supported":[108,140],"by":[109,141],"Deutsche":[111],"Forschungsgemeinschaft":[112],"(DFG,":[113],"German":[114],"Foundation)":[116],"under":[117],"Germany\u2019s":[118],"Excellence":[119],"Strategy\u2014The":[120],"Berlin":[121],"Mathematics":[122],"Center":[124],"MATH":[125],"(EXC-2046/1,":[126],"project":[127],"ID":[128],"390685689,":[129],"BMS":[130],"Stipend).":[131],"also":[138],"Bajaj":[143],"Family":[144],"Chair":[145],"at":[146],"Tepper":[148],"School":[149],"Business,":[151],"Carnegie":[152],"Mellon":[153],"University.":[154]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}