{"id":"https://openalex.org/W4386711481","doi":"https://doi.org/10.1080/02331934.2023.2257709","title":"A generalized conditional gradient method for multiobjective composite optimization problems","display_name":"A generalized conditional gradient method for multiobjective composite optimization problems","publication_year":2023,"publication_date":"2023-09-13","ids":{"openalex":"https://openalex.org/W4386711481","doi":"https://doi.org/10.1080/02331934.2023.2257709"},"language":"en","primary_location":{"id":"doi:10.1080/02331934.2023.2257709","doi":"https://doi.org/10.1080/02331934.2023.2257709","is_oa":false,"landing_page_url":"https://doi.org/10.1080/02331934.2023.2257709","pdf_url":null,"source":{"id":"https://openalex.org/S158016561","display_name":"Optimization","issn_l":"0233-1934","issn":["0233-1934","1026-7662","1029-4945"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-c","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2302.12912","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029517240","display_name":"P. B. Assun\u00e7\u00e3o","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I68106152","display_name":"Universidade Federal de Goi\u00e1s","ror":"https://ror.org/0039d5757","country_code":"BR","type":"education","lineage":["https://openalex.org/I68106152"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"P. B. Assun\u00e7\u00e3o","raw_affiliation_strings":["Universidade Federal de Goi\u00e1s","Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, Goi\u00e2nia, GO, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Federal de Goi\u00e1s","institution_ids":["https://openalex.org/I68106152"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, Goi\u00e2nia, GO, Brazil","institution_ids":["https://openalex.org/I68106152"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026963153","display_name":"O. P. Ferreira","orcid":"https://orcid.org/0000-0002-5758-0320","observed_orcids":["https://orcid.org/0000-0002-5758-0320"]},"institutions":[{"id":"https://openalex.org/I68106152","display_name":"Universidade Federal de Goi\u00e1s","ror":"https://ror.org/0039d5757","country_code":"BR","type":"education","lineage":["https://openalex.org/I68106152"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"O. P. Ferreira","raw_affiliation_strings":["Universidade Federal de Goi\u00e1s","Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, Goi\u00e2nia, GO, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-5758-0320","affiliations":[{"raw_affiliation_string":"Universidade Federal de Goi\u00e1s","institution_ids":["https://openalex.org/I68106152"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, Goi\u00e2nia, GO, Brazil","institution_ids":["https://openalex.org/I68106152"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064624706","display_name":"L. F. Prudente","orcid":"https://orcid.org/0000-0003-1098-4317","observed_orcids":["https://orcid.org/0000-0003-1098-4317"]},"institutions":[{"id":"https://openalex.org/I68106152","display_name":"Universidade Federal de Goi\u00e1s","ror":"https://ror.org/0039d5757","country_code":"BR","type":"education","lineage":["https://openalex.org/I68106152"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"L. F. Prudente","raw_affiliation_strings":["Universidade Federal de Goi\u00e1s","Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, Goi\u00e2nia, GO, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-1098-4317","affiliations":[{"raw_affiliation_string":"Universidade Federal de Goi\u00e1s","institution_ids":["https://openalex.org/I68106152"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica e Estat\u00edstica, Universidade Federal de Goi\u00e1s, Goi\u00e2nia, GO, Brazil","institution_ids":["https://openalex.org/I68106152"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5026963153"],"corresponding_institution_ids":["https://openalex.org/I68106152"],"apc_list":null,"apc_paid":null,"fwci":2.8626,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.91232711,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"74","issue":"2","first_page":"473","last_page":"503"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7914999723434448,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.7914999723434448,"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":0.16140000522136688,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.032099999487400055,"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/frank-wolfe-algorithm","display_name":"Frank-Wolfe algorithm","score":0.9940000176429749},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"multi-objective optimization","score":0.996999979019165},{"id":"https://openalex.org/keywords/composite-optimization","display_name":"composite optimization","score":0.9649999737739563},{"id":"https://openalex.org/keywords/nonsmooth-functions","display_name":"nonsmooth functions","score":0.8349999785423279},{"id":"https://openalex.org/keywords/adaptive-step-size","display_name":"adaptive step size","score":0.8809999823570251},{"id":"https://openalex.org/keywords/diminishing-step-size","display_name":"diminishing step size","score":0.9769999980926514},{"id":"https://openalex.org/keywords/asymptotic-convergence","display_name":"asymptotic convergence","score":0.9020000100135803},{"id":"https://openalex.org/keywords/iteration-complexity","display_name":"iteration complexity","score":0.7089999914169312},{"id":"https://openalex.org/keywords/convexity-assumptions","display_name":"convexity assumptions","score":0.6399999856948853}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6852902173995972},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6344659328460693},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6135022640228271},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5657352805137634},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4851270616054535},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.43918728828430176},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3910200595855713},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3421397805213928},{"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/02331934.2023.2257709","doi":"https://doi.org/10.1080/02331934.2023.2257709","is_oa":false,"landing_page_url":"https://doi.org/10.1080/02331934.2023.2257709","pdf_url":null,"source":{"id":"https://openalex.org/S158016561","display_name":"Optimization","issn_l":"0233-1934","issn":["0233-1934","1026-7662","1029-4945"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-c","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2302.12912","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2302.12912","pdf_url":"https://arxiv.org/pdf/2302.12912","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2302.12912","doi":"https://doi.org/10.48550/arxiv.2302.12912","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2302.12912","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2302.12912","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2302.12912","pdf_url":"https://arxiv.org/pdf/2302.12912","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2255545593","display_name":null,"funder_award_id":"305158/2014-7","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G7647985512","display_name":null,"funder_award_id":"302473/2017-3","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"},{"id":"https://openalex.org/G8972730898","display_name":null,"funder_award_id":"304666/2021-1, 305158/2014-7","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386711481.pdf","grobid_xml":"https://content.openalex.org/works/W4386711481.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W1606015457","https://openalex.org/W1842733265","https://openalex.org/W1969244384","https://openalex.org/W1970895334","https://openalex.org/W1980432290","https://openalex.org/W1994569450","https://openalex.org/W2004586020","https://openalex.org/W2013243898","https://openalex.org/W2024008934","https://openalex.org/W2032571239","https://openalex.org/W2050358508","https://openalex.org/W2052471135","https://openalex.org/W2056603712","https://openalex.org/W2063375245","https://openalex.org/W2064114515","https://openalex.org/W2067252707","https://openalex.org/W2081313036","https://openalex.org/W2088140565","https://openalex.org/W2098593811","https://openalex.org/W2100717205","https://openalex.org/W2117411467","https://openalex.org/W2125899728","https://openalex.org/W2127519119","https://openalex.org/W2143185749","https://openalex.org/W2149454052","https://openalex.org/W2149726897","https://openalex.org/W2153015072","https://openalex.org/W2225671745","https://openalex.org/W2531315337","https://openalex.org/W2561080469","https://openalex.org/W2739128850","https://openalex.org/W2790326975","https://openalex.org/W2796881136","https://openalex.org/W2803933598","https://openalex.org/W2889351029","https://openalex.org/W2893010165","https://openalex.org/W2899313272","https://openalex.org/W2903140114","https://openalex.org/W2960169247","https://openalex.org/W2976995972","https://openalex.org/W2994752162","https://openalex.org/W3046534822","https://openalex.org/W3123714067","https://openalex.org/W4211111980","https://openalex.org/W4224309194","https://openalex.org/W4241673740","https://openalex.org/W4280533413","https://openalex.org/W4286005551","https://openalex.org/W4296182520","https://openalex.org/W4313575371","https://openalex.org/W4379958599","https://openalex.org/W4383368610"],"related_works":["https://openalex.org/W7138302705","https://openalex.org/W3123714067","https://openalex.org/W4410460921","https://openalex.org/W4411437105","https://openalex.org/W4408461967","https://openalex.org/W4387260731","https://openalex.org/W2146482778","https://openalex.org/W4414120904","https://openalex.org/W2264518955","https://openalex.org/W4417450616"],"abstract_inverted_index":{"This":[0],"article":[1],"deals":[2],"with":[3,52,72],"multiobjective":[4],"composite":[5],"optimization":[6],"problems":[7],"that":[8],"consist":[9],"of":[10,17,21,24,38,87],"simultaneously":[11],"minimizing":[12],"several":[13],"objective":[14,79],"functions,":[15],"each":[16],"which":[18],"is":[19,50],"composed":[20],"a":[22,35],"combination":[23],"smooth":[25],"and":[26,60,69,73],"non-smooth":[27],"functions.":[28,80],"To":[29],"tackle":[30],"these":[31],"problems,":[32],"we":[33],"propose":[34],"generalized":[36],"version":[37],"the":[39,78,84,88],"conditional":[40],"gradient":[41],"method,":[42],"also":[43],"known":[44],"as":[45],"Frank-Wolfe":[46],"method.":[47],"The":[48],"method":[49],"analysed":[51],"three":[53],"step":[54,62],"size":[55],"strategies,":[56],"including":[57],"Armijo-type,":[58],"adaptive,":[59],"diminishing":[61],"sizes.":[63],"We":[64],"establish":[65],"asymptotic":[66],"convergence":[67],"properties":[68],"iteration-complexity":[70],"bounds,":[71],"without":[74],"convexity":[75],"assumptions":[76],"on":[77],"Numerical":[81],"experiments":[82],"illustrating":[83],"practical":[85],"behaviour":[86],"methods":[89],"are":[90],"presented.":[91]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2023-09-14T00:00:00"}