{"id":"https://openalex.org/W2783144925","doi":"https://doi.org/10.1007/s10589-019-00106-9","title":"Non-stationary Douglas\u2013Rachford and alternating direction method of multipliers: adaptive step-sizes and convergence","display_name":"Non-stationary Douglas\u2013Rachford and alternating direction method of multipliers: adaptive step-sizes and convergence","publication_year":2019,"publication_date":"2019-05-08","ids":{"openalex":"https://openalex.org/W2783144925","doi":"https://doi.org/10.1007/s10589-019-00106-9","mag":"2783144925"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-019-00106-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-019-00106-9","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1801.03765","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069699303","display_name":"Dirk A. Lorenz","orcid":"https://orcid.org/0000-0002-7419-769X"},"institutions":[{"id":"https://openalex.org/I94509681","display_name":"Technische Universit\u00e4t Braunschweig","ror":"https://ror.org/010nsgg66","country_code":"DE","type":"education","lineage":["https://openalex.org/I94509681"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Dirk A. Lorenz","raw_affiliation_strings":["Institute of Analysis and Algebra, TU Braunschweig, 38092, Braunschweig, Germany"],"raw_orcid":"https://orcid.org/0000-0002-7419-769X","affiliations":[{"raw_affiliation_string":"Institute of Analysis and Algebra, TU Braunschweig, 38092, Braunschweig, Germany","institution_ids":["https://openalex.org/I94509681"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056282016","display_name":"Quoc Tran-Dinh","orcid":"https://orcid.org/0000-0002-1077-2579"},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Quoc Tran-Dinh","raw_affiliation_strings":["Department of Statistics and Operations Research, University of North Carolina at Chapel Hill (UNC-Chapel Hill), 333 Hanes Hall, CB# 3260, UNC Chapel Hill, NC, 27599-3260, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, University of North Carolina at Chapel Hill (UNC-Chapel Hill), 333 Hanes Hall, CB# 3260, UNC Chapel Hill, NC, 27599-3260, USA","institution_ids":["https://openalex.org/I114027177"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069699303"],"corresponding_institution_ids":["https://openalex.org/I94509681"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.3787,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.48356425,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"74","issue":"1","first_page":"67","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987000226974487,"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"}},{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9984999895095825,"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/convergence","display_name":"Convergence (economics)","score":0.741582453250885},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6403597593307495},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6300371885299683},{"id":"https://openalex.org/keywords/adaptive-stepsize","display_name":"Adaptive stepsize","score":0.6184791326522827},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5290029644966125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5202904343605042},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.41302600502967834},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.40726733207702637},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40008631348609924},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.21864739060401917},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18063905835151672}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.741582453250885},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6403597593307495},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6300371885299683},{"id":"https://openalex.org/C48077252","wikidata":"https://www.wikidata.org/wiki/Q4680766","display_name":"Adaptive stepsize","level":3,"score":0.6184791326522827},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5290029644966125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5202904343605042},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.41302600502967834},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.40726733207702637},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40008631348609924},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.21864739060401917},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18063905835151672},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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":5,"locations":[{"id":"doi:10.1007/s10589-019-00106-9","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10589-019-00106-9","pdf_url":null,"source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1801.03765","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.03765","pdf_url":"https://arxiv.org/pdf/1801.03765","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2783144925","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1801.03765.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:RePEc:spr:coopap:v:74:y:2019:i:1:d:10.1007_s10589-019-00106-9","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-019-00106-9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"doi:10.48550/arxiv.1801.03765","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1801.03765","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1801.03765","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.03765","pdf_url":"https://arxiv.org/pdf/1801.03765","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1774196161","display_name":null,"funder_award_id":"1127914","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"},{"id":"https://openalex.org/G4123259794","display_name":null,"funder_award_id":"1127914","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4820226482","display_name":null,"funder_award_id":"DMS-1127914","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"},{"id":"https://openalex.org/G7028128371","display_name":null,"funder_award_id":"DMS-161984","funder_id":"https://openalex.org/F4320332172","funder_display_name":"Directorate for Mathematical and Physical Sciences"},{"id":"https://openalex.org/G8280225390","display_name":null,"funder_award_id":"DMS-1127914","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8492689677","display_name":null,"funder_award_id":"DMS-1127914","funder_id":"https://openalex.org/F4320337380","funder_display_name":"Division of Mathematical Sciences"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2783144925.pdf","grobid_xml":"https://content.openalex.org/works/W2783144925.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W845484681","https://openalex.org/W1160395089","https://openalex.org/W1504715377","https://openalex.org/W1562101002","https://openalex.org/W1607518970","https://openalex.org/W1897801518","https://openalex.org/W1922736325","https://openalex.org/W1966333543","https://openalex.org/W1967317714","https://openalex.org/W1969128975","https://openalex.org/W1984680242","https://openalex.org/W1984845675","https://openalex.org/W1986080131","https://openalex.org/W2003372231","https://openalex.org/W2019569173","https://openalex.org/W2021548137","https://openalex.org/W2037603831","https://openalex.org/W2038497950","https://openalex.org/W2056510226","https://openalex.org/W2058532290","https://openalex.org/W2059189829","https://openalex.org/W2074214991","https://openalex.org/W2100556411","https://openalex.org/W2101393121","https://openalex.org/W2103559027","https://openalex.org/W2119058682","https://openalex.org/W2135046866","https://openalex.org/W2142280715","https://openalex.org/W2158449358","https://openalex.org/W2164278908","https://openalex.org/W2216134724","https://openalex.org/W2336965487","https://openalex.org/W2395947128","https://openalex.org/W2580889931","https://openalex.org/W2605753231","https://openalex.org/W2798909945","https://openalex.org/W2804781295","https://openalex.org/W2891877934","https://openalex.org/W2951085447","https://openalex.org/W2962964459","https://openalex.org/W2962982726","https://openalex.org/W2963000588","https://openalex.org/W2963512942","https://openalex.org/W2964266105","https://openalex.org/W3099831354","https://openalex.org/W4292363360","https://openalex.org/W4312258136","https://openalex.org/W6600011198","https://openalex.org/W6604285789","https://openalex.org/W6677804474","https://openalex.org/W6776883395","https://openalex.org/W6838354976"],"related_works":["https://openalex.org/W2963286475","https://openalex.org/W182096945","https://openalex.org/W1999393886","https://openalex.org/W3104046271","https://openalex.org/W2389751445","https://openalex.org/W1562505150","https://openalex.org/W2969830504","https://openalex.org/W2918202932","https://openalex.org/W2286297039","https://openalex.org/W1825307613","https://openalex.org/W2782341585","https://openalex.org/W1986080131","https://openalex.org/W3109568406","https://openalex.org/W2951408483","https://openalex.org/W2255188617","https://openalex.org/W2149316982","https://openalex.org/W2352827409","https://openalex.org/W2776251461","https://openalex.org/W3039509295","https://openalex.org/W2987613135"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
