{"id":"https://openalex.org/W2011746047","doi":"https://doi.org/10.1016/s0377-2217(02)00629-x","title":"On the convergence of conditional \u03b5-subgradient methods for convex programs and convex\u2013concave saddle-point problems","display_name":"On the convergence of conditional \u03b5-subgradient methods for convex programs and convex\u2013concave saddle-point problems","publication_year":2003,"publication_date":"2003-04-07","ids":{"openalex":"https://openalex.org/W2011746047","doi":"https://doi.org/10.1016/s0377-2217(02)00629-x","mag":"2011746047"},"language":"en","primary_location":{"id":"doi:10.1016/s0377-2217(02)00629-x","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0377-2217(02)00629-x","pdf_url":null,"source":{"id":"https://openalex.org/S103321696","display_name":"European Journal of Operational Research","issn_l":"0377-2217","issn":["0377-2217","1872-6860"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Operational 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/A5074200057","display_name":"Torbj\u00f6rn Larsson","orcid":"https://orcid.org/0000-0003-2094-7376"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Torbj\u00f6rn Larsson","raw_affiliation_strings":["Department of Mathematics, Link\u00f6ping University, SE-581 83 Link\u00f6ping, Sweden","Department of Mathematics, Link\u00f6ping University, SE-581 83 Link\u00f6ping, Sweden,"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Link\u00f6ping University, SE-581 83 Link\u00f6ping, Sweden","institution_ids":["https://openalex.org/I102134673"]},{"raw_affiliation_string":"Department of Mathematics, Link\u00f6ping University, SE-581 83 Link\u00f6ping, Sweden,","institution_ids":["https://openalex.org/I102134673"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008055628","display_name":"Michael Patriksson","orcid":"https://orcid.org/0000-0001-7675-7454"},"institutions":[{"id":"https://openalex.org/I66862912","display_name":"Chalmers University of Technology","ror":"https://ror.org/040wg7k59","country_code":"SE","type":"education","lineage":["https://openalex.org/I66862912"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Michael Patriksson","raw_affiliation_strings":["Department of Mathematics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden","Department of Mathematics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden","institution_ids":["https://openalex.org/I66862912"]},{"raw_affiliation_string":"Department of Mathematics, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden#TAB#","institution_ids":["https://openalex.org/I66862912"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049531929","display_name":"Ann\u2010Brith Str\u00f6mberg","orcid":"https://orcid.org/0000-0003-1962-7279"},"institutions":[{"id":"https://openalex.org/I4210139723","display_name":"Fraunhofer Chalmers Research Centre for Industrial Mathematics","ror":"https://ror.org/03tqh5n18","country_code":"SE","type":"nonprofit","lineage":["https://openalex.org/I4210139723","https://openalex.org/I4923324"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Ann-Brith Str\u00f6mberg","raw_affiliation_strings":["Fraunhofer\u2013Chalmers Research Center for Industrial Mathematics, SE-412 88 Gothenburg, Sweden"],"affiliations":[{"raw_affiliation_string":"Fraunhofer\u2013Chalmers Research Center for Industrial Mathematics, SE-412 88 Gothenburg, Sweden","institution_ids":["https://openalex.org/I4210139723"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008055628"],"corresponding_institution_ids":["https://openalex.org/I66862912"],"apc_list":{"value":3290,"currency":"USD","value_usd":3290},"apc_paid":null,"fwci":3.4607,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.92529412,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"151","issue":"3","first_page":"461","last_page":"473"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9980999827384949,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9825000166893005,"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/subgradient-method","display_name":"Subgradient method","score":0.9428152441978455},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.7878845930099487},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7054617404937744},{"id":"https://openalex.org/keywords/saddle","display_name":"Saddle","score":0.6101744771003723},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5638496279716492},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5378209352493286},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.48933786153793335},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.48865488171577454},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.48679444193840027},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46667444705963135},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45920875668525696},{"id":"https://openalex.org/keywords/frank\u2013wolfe-algorithm","display_name":"Frank\u2013Wolfe algorithm","score":0.4218471944332123},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18837371468544006},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.15116244554519653},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06455299258232117}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.9428152441978455},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7878845930099487},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7054617404937744},{"id":"https://openalex.org/C2777127463","wikidata":"https://www.wikidata.org/wiki/Q10862618","display_name":"Saddle","level":2,"score":0.6101744771003723},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5638496279716492},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5378209352493286},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.48933786153793335},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.48865488171577454},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.48679444193840027},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46667444705963135},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45920875668525696},{"id":"https://openalex.org/C122268817","wikidata":"https://www.wikidata.org/wiki/Q2020318","display_name":"Frank\u2013Wolfe algorithm","level":5,"score":0.4218471944332123},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18837371468544006},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.15116244554519653},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06455299258232117},{"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":3,"locations":[{"id":"doi:10.1016/s0377-2217(02)00629-x","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0377-2217(02)00629-x","pdf_url":null,"source":{"id":"https://openalex.org/S103321696","display_name":"European Journal of Operational Research","issn_l":"0377-2217","issn":["0377-2217","1872-6860"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"European Journal of Operational Research","raw_type":"journal-article"},{"id":"pmh:oai:fraunhofer.de:N-37374","is_oa":false,"landing_page_url":"http://publica.fraunhofer.de/documents/N-37374.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400801","display_name":"Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fraunhofer ITWM","raw_type":"Journal Article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/203285","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/203285","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"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":33,"referenced_works":["https://openalex.org/W258481170","https://openalex.org/W431765274","https://openalex.org/W585015008","https://openalex.org/W1481747975","https://openalex.org/W1551892507","https://openalex.org/W1554465673","https://openalex.org/W1568288633","https://openalex.org/W1971290991","https://openalex.org/W1975666048","https://openalex.org/W1986624101","https://openalex.org/W1996903464","https://openalex.org/W1997231674","https://openalex.org/W2007255736","https://openalex.org/W2015263936","https://openalex.org/W2031583508","https://openalex.org/W2032606187","https://openalex.org/W2041221438","https://openalex.org/W2045269330","https://openalex.org/W2050014122","https://openalex.org/W2050388101","https://openalex.org/W2061657011","https://openalex.org/W2073819859","https://openalex.org/W2083432309","https://openalex.org/W2091604953","https://openalex.org/W2093991669","https://openalex.org/W2121676328","https://openalex.org/W2130469840","https://openalex.org/W2325681654","https://openalex.org/W2336259629","https://openalex.org/W2787523326","https://openalex.org/W2798766386","https://openalex.org/W4211092921","https://openalex.org/W4230344464"],"related_works":["https://openalex.org/W1758974965","https://openalex.org/W4298155671","https://openalex.org/W4236459141","https://openalex.org/W4205304778","https://openalex.org/W2020252434","https://openalex.org/W73248859","https://openalex.org/W2188090572","https://openalex.org/W2584253892","https://openalex.org/W2350324449","https://openalex.org/W119381072"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}