{"id":"https://openalex.org/W3043378690","doi":"https://doi.org/10.1080/10556788.2020.1786564","title":"On the complexity of solving feasibility problems with regularized models","display_name":"On the complexity of solving feasibility problems with regularized models","publication_year":2020,"publication_date":"2020-07-13","ids":{"openalex":"https://openalex.org/W3043378690","doi":"https://doi.org/10.1080/10556788.2020.1786564","mag":"3043378690"},"language":"en","primary_location":{"id":"doi:10.1080/10556788.2020.1786564","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2020.1786564","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5087290455","display_name":"Ernesto G. Birgin","orcid":"https://orcid.org/0000-0002-7466-7663"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]},{"id":"https://openalex.org/I4210092357","display_name":"Institute of Mathematics and Computer Science","ror":"https://ror.org/00fy4at53","country_code":"MD","type":"facility","lineage":["https://openalex.org/I112090838","https://openalex.org/I4210092357"]}],"countries":["BR","MD"],"is_corresponding":true,"raw_author_name":"E. G. Birgin","raw_affiliation_strings":["Department of Computer Science, Institute of Mathematics and Statistics, University of S\u00e3o Paulo","Department of Computer Science, Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-7466-7663","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Institute of Mathematics and Statistics, University of S\u00e3o Paulo","institution_ids":["https://openalex.org/I4210092357","https://openalex.org/I17974374"]},{"raw_affiliation_string":"Department of Computer Science, Institute of Mathematics and Statistics, University of S\u00e3o Paulo, S\u00e3o Paulo, Brazil","institution_ids":["https://openalex.org/I17974374"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008833621","display_name":"L. F. Bueno","orcid":"https://orcid.org/0000-0002-8820-6606"},"institutions":[{"id":"https://openalex.org/I88273585","display_name":"Universidade Federal de S\u00e3o Paulo","ror":"https://ror.org/02k5swt12","country_code":"BR","type":"education","lineage":["https://openalex.org/I88273585"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"L. F. Bueno","raw_affiliation_strings":["Department of Science and Technology, Federal University of S\u00e3o Paulo","Department of Science and Technology, Federal University of S\u00e3o Paulo, S\u00e3o Jos\u00e9 dos Campos, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-8820-6606","affiliations":[{"raw_affiliation_string":"Department of Science and Technology, Federal University of S\u00e3o Paulo","institution_ids":["https://openalex.org/I88273585"]},{"raw_affiliation_string":"Department of Science and Technology, Federal University of S\u00e3o Paulo, S\u00e3o Jos\u00e9 dos Campos, Brazil","institution_ids":["https://openalex.org/I88273585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066019994","display_name":"J. M. Mart\u0131\u0301nez","orcid":"https://orcid.org/0000-0003-3331-368X"},"institutions":[{"id":"https://openalex.org/I181391015","display_name":"Universidade Estadual de Campinas (UNICAMP)","ror":"https://ror.org/04wffgt70","country_code":"BR","type":"education","lineage":["https://openalex.org/I181391015"]},{"id":"https://openalex.org/I4210120266","display_name":"Czech Academy of Sciences, Institute of Mathematics","ror":"https://ror.org/02tv1yf50","country_code":"CZ","type":"facility","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210120266"]}],"countries":["BR","CZ"],"is_corresponding":false,"raw_author_name":"J. M. Mart\u00ednez","raw_affiliation_strings":["Department of Applied Mathematics, Institute of Mathematics, Statistics, and Scientific Computing, State University of Campinas","Department of Applied Mathematics, Institute of Mathematics, Statistics, and Scientific Computing, State University of Campinas, Campinas, Brazil"],"raw_orcid":"https://orcid.org/0000-0003-3331-368X","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Institute of Mathematics, Statistics, and Scientific Computing, State University of Campinas","institution_ids":["https://openalex.org/I4210120266","https://openalex.org/I181391015"]},{"raw_affiliation_string":"Department of Applied Mathematics, Institute of Mathematics, Statistics, and Scientific Computing, State University of Campinas, Campinas, Brazil","institution_ids":["https://openalex.org/I181391015"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087290455"],"corresponding_institution_ids":["https://openalex.org/I17974374","https://openalex.org/I4210092357"],"apc_list":null,"apc_paid":null,"fwci":0.2956,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.51458333,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"37","issue":"2","first_page":"405","last_page":"424"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9984999895095825,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9909999966621399,"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/computer-science","display_name":"Computer science","score":0.4889775514602661},{"id":"https://openalex.org/keywords/management-science","display_name":"Management science","score":0.4173336327075958},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.18364766240119934}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4889775514602661},{"id":"https://openalex.org/C539667460","wikidata":"https://www.wikidata.org/wiki/Q2414942","display_name":"Management science","level":1,"score":0.4173336327075958},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.18364766240119934}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556788.2020.1786564","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556788.2020.1786564","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Decent work and economic growth","score":0.46000000834465027,"id":"https://metadata.un.org/sdg/8"}],"awards":[{"id":"https://openalex.org/G305158216","display_name":null,"funder_award_id":"2016/01860-1","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G4208676761","display_name":null,"funder_award_id":"2018/24293-0","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"},{"id":"https://openalex.org/G5990746028","display_name":null,"funder_award_id":"2013/07375-0","funder_id":"https://openalex.org/F4320320997","funder_display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo"}],"funders":[{"id":"https://openalex.org/F4320320997","display_name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","ror":"https://ror.org/02ddkpn78"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W189211379","https://openalex.org/W646582900","https://openalex.org/W1973734200","https://openalex.org/W1987995897","https://openalex.org/W1994974865","https://openalex.org/W2003949305","https://openalex.org/W2009941369","https://openalex.org/W2012341322","https://openalex.org/W2057565823","https://openalex.org/W2068484625","https://openalex.org/W2076605490","https://openalex.org/W2128736738","https://openalex.org/W2156005216","https://openalex.org/W2165393620","https://openalex.org/W2272094913","https://openalex.org/W2510806995","https://openalex.org/W2599851351","https://openalex.org/W2774800844","https://openalex.org/W2792215433","https://openalex.org/W2955809168","https://openalex.org/W3014094092","https://openalex.org/W3021249612","https://openalex.org/W3103316059","https://openalex.org/W4241760093","https://openalex.org/W4298062829"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W2382290278","https://openalex.org/W2478288626","https://openalex.org/W4391913857","https://openalex.org/W2350741829","https://openalex.org/W2530322880"],"abstract_inverted_index":{"The":[0],"complexity":[1,108,112],"of":[2,40,43,45,66,91,95,97,150],"solving":[3],"feasibility":[4],"problems":[5],"is":[6,12,71,86],"considered":[7],"in":[8],"this":[9],"work.":[10],"It":[11],"assumed":[13],"that":[14,17,73,85],"the":[15,19,32,41,46,51,63,67,93,98,103,114,132],"constraints":[16,48,100,105],"define":[18],"problem":[20],"can":[21],"be":[22],"divided":[23],"into":[24],"expensive":[25,47,68,99,115],"and":[26,110,120,138],"cheap":[27,52,104],"constraints.":[28,53],"At":[29],"each":[30],"iteration,":[31],"introduced":[33],"method":[34],"minimizes":[35],"a":[36,55,75,135,139],"regularized":[37],"pth-order":[38],"model":[39],"sum":[42,94],"squares":[44,96],"subject":[49,101],"to":[50,102,147],"Under":[54],"H\u00f6lder":[56],"continuity":[57],"property":[58],"with":[59,78,88],"constant":[60],"\u03b2\u2208(0,1]":[61],"on":[62],"pth":[64],"derivatives":[65,133],"constraints,":[69],"it":[70],"shown":[72],"finding":[74],"feasible":[76],"point":[77,84],"precision":[79],"\u03b5>0":[80],"or":[81],"an":[82],"infeasible":[83],"stationary":[87],"tolerance":[89],"\u03b3>0":[90],"minimizing":[92],"has":[106],"iteration":[107],"O(|log\u2061(\u03b5)|\u03b3\u03b6(p,\u03b2)\u03c9p1+(1/2)\u03b6(p,\u03b2))":[109],"evaluation":[111],"(of":[113],"constraints)":[116],"O(|log\u2061(\u03b5)|[\u03b3\u03b6(p,\u03b2)\u03c9p1+(1/2)\u03b6(p,\u03b2)+(1\u2212\u03b2)/(p+\u03b2\u22121)|log\u2061(\u03b3\u03b5)|]),":[117],"where":[118],"\u03b6(p,\u03b2)=\u2212(p+\u03b2)/(p+\u03b2\u22121)":[119],"\u03c9p=\u03b5":[121],"if":[122,128,131],"p":[123],"=":[124],"1,":[125],"while":[126],"\u03c9p=\u03a6(x0)":[127],"p>1.":[129],"Moreover,":[130],"satisfy":[134],"Lipschitz":[136],"condition":[137],"uniform":[140],"regularity":[141],"assumption":[142],"holds,":[143],"both":[144],"complexities":[145],"reduce":[146],"O(|log\u2061(\u03b5)|),":[148],"independently":[149],"p.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2020-07-23T00:00:00"}
