{"id":"https://openalex.org/W2041221438","doi":"https://doi.org/10.1007/s101070050090","title":"Ergodic, primal convergence in dual subgradient schemes for convex programming","display_name":"Ergodic, primal convergence in dual subgradient schemes for convex programming","publication_year":1999,"publication_date":"1999-11-01","ids":{"openalex":"https://openalex.org/W2041221438","doi":"https://doi.org/10.1007/s101070050090","mag":"2041221438"},"language":"en","primary_location":{"id":"doi:10.1007/s101070050090","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s101070050090","pdf_url":null,"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":null,"license_id":null,"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":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":["Division of Optimization, Department of Mathematics, Link\u00f6ping University, S-581 83 Link\u00f6ping, Sweden, , , , , , SE","Division of Optimization, Department of Mathematics, Link\u00f6ping University, S-581 83 Link\u00f6ping, Sweden, SE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Optimization, Department of Mathematics, Link\u00f6ping University, S-581 83 Link\u00f6ping, Sweden, , , , , , SE","institution_ids":["https://openalex.org/I102134673"]},{"raw_affiliation_string":"Division of Optimization, Department of Mathematics, Link\u00f6ping University, S-581 83 Link\u00f6ping, Sweden, SE","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":false,"raw_author_name":"Michael Patriksson","raw_affiliation_strings":["Department of Mathematics, Chalmers University of Technology, S-412 96 G\u00f6teborg, Sweden, Fax: +46 31 16 19 73, e-mail: anstr@math.chalmers.se, , , , , , SE","Department of Mathematics, Chalmers University of Technology, S-412 96 G\u00f6teborg, Sweden, Fax: +46 31 16 19 73, e-mail: anstr@math.chalmers.se, SE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chalmers University of Technology, S-412 96 G\u00f6teborg, Sweden, Fax: +46 31 16 19 73, e-mail: anstr@math.chalmers.se, , , , , , SE","institution_ids":["https://openalex.org/I66862912"]},{"raw_affiliation_string":"Department of Mathematics, Chalmers University of Technology, S-412 96 G\u00f6teborg, Sweden, Fax: +46 31 16 19 73, e-mail: anstr@math.chalmers.se, SE","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/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":false,"raw_author_name":"Ann-Brith Str\u00f6mberg","raw_affiliation_strings":["Department of Mathematics, Chalmers University of Technology, S-412 96 G\u00f6teborg, Sweden, Fax: +46 31 16 19 73, e-mail: anstr@math.chalmers.se, , , , , , SE","Department of Mathematics, Chalmers University of Technology, S-412 96 G\u00f6teborg, Sweden, Fax: +46 31 16 19 73, e-mail: anstr@math.chalmers.se, SE"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chalmers University of Technology, S-412 96 G\u00f6teborg, Sweden, Fax: +46 31 16 19 73, e-mail: anstr@math.chalmers.se, , , , , , SE","institution_ids":["https://openalex.org/I66862912"]},{"raw_affiliation_string":"Department of Mathematics, Chalmers University of Technology, S-412 96 G\u00f6teborg, Sweden, Fax: +46 31 16 19 73, e-mail: anstr@math.chalmers.se, SE","institution_ids":["https://openalex.org/I66862912"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":17.2901,"has_fulltext":false,"cited_by_count":137,"citation_normalized_percentile":{"value":0.9855383,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"86","issue":"2","first_page":"283","last_page":"312"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10698","display_name":"Transportation Planning and Optimization","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12546","display_name":"Smart Parking Systems Research","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2215","display_name":"Building and Construction"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9883000254631042,"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":0.9643487334251404},{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.7404117584228516},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7284716367721558},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6698060035705566},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5798633098602295},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5789013504981995},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5203002095222473},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4192044138908386},{"id":"https://openalex.org/keywords/lagrangian-relaxation","display_name":"Lagrangian relaxation","score":0.41091281175613403},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3486648499965668}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.9643487334251404},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7404117584228516},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7284716367721558},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6698060035705566},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5798633098602295},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5789013504981995},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5203002095222473},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4192044138908386},{"id":"https://openalex.org/C91765299","wikidata":"https://www.wikidata.org/wiki/Q3424292","display_name":"Lagrangian relaxation","level":2,"score":0.41091281175613403},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3486648499965668},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s101070050090","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s101070050090","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.476.1086","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.476.1086","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://publications.lib.chalmers.se/records/fulltext/local_141625.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.51.4036","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.4036","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.chalmers.se/~mipat/./LATEX/Dualerg.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.610.6562","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.610.6562","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.chalmers.se/Math/Grundutb/CTH/tma521/0506/erg.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.63.5771","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.5771","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.chalmers.se/~mipat/LATEX/Dualerg.pdf","raw_type":"text"},{"id":"pmh:oai:research.chalmers.se:502055","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/0829d059-1a92-444b-ad86-1a5b1a23f944","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W1429901","https://openalex.org/W121392136","https://openalex.org/W313242074","https://openalex.org/W624120492","https://openalex.org/W1481747975","https://openalex.org/W1559215823","https://openalex.org/W1574558330","https://openalex.org/W1574923065","https://openalex.org/W1603765807","https://openalex.org/W1669104078","https://openalex.org/W1876995267","https://openalex.org/W1971290991","https://openalex.org/W1972292407","https://openalex.org/W1974893068","https://openalex.org/W1975666048","https://openalex.org/W1986624101","https://openalex.org/W1997231674","https://openalex.org/W1999635659","https://openalex.org/W2003912133","https://openalex.org/W2015263936","https://openalex.org/W2016824559","https://openalex.org/W2019340883","https://openalex.org/W2020317140","https://openalex.org/W2032606187","https://openalex.org/W2033468335","https://openalex.org/W2038606782","https://openalex.org/W2040358553","https://openalex.org/W2043270922","https://openalex.org/W2045269330","https://openalex.org/W2055978654","https://openalex.org/W2063856759","https://openalex.org/W2064948689","https://openalex.org/W2069277547","https://openalex.org/W2073219008","https://openalex.org/W2073819859","https://openalex.org/W2081636333","https://openalex.org/W2083431420","https://openalex.org/W2087338175","https://openalex.org/W2105560970","https://openalex.org/W2107367810","https://openalex.org/W2108303241","https://openalex.org/W2114844199","https://openalex.org/W2117379131","https://openalex.org/W2121676328","https://openalex.org/W2125645230","https://openalex.org/W2130300008","https://openalex.org/W2130469840","https://openalex.org/W2135779729","https://openalex.org/W2139211712","https://openalex.org/W2168405789","https://openalex.org/W2175706438","https://openalex.org/W2325681654","https://openalex.org/W2395106057","https://openalex.org/W2407047152","https://openalex.org/W2475559389","https://openalex.org/W2595897327","https://openalex.org/W2798766386","https://openalex.org/W3106807711","https://openalex.org/W3141390961","https://openalex.org/W4230214681","https://openalex.org/W4236384091","https://openalex.org/W4242576043","https://openalex.org/W4256046638","https://openalex.org/W4300549156","https://openalex.org/W4375818997"],"related_works":["https://openalex.org/W2037613239","https://openalex.org/W3183857959","https://openalex.org/W4243844638","https://openalex.org/W2894990380","https://openalex.org/W195910675","https://openalex.org/W3032916910","https://openalex.org/W2363143319","https://openalex.org/W2351035339","https://openalex.org/W1980006501","https://openalex.org/W2138760184"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":8}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}