{"id":"https://openalex.org/W2625294292","doi":"https://doi.org/10.1007/s10898-018-0677-3","title":"A Lyapunov-type approach to convergence of the Douglas\u2013Rachford algorithm for a nonconvex setting","display_name":"A Lyapunov-type approach to convergence of the Douglas\u2013Rachford algorithm for a nonconvex setting","publication_year":2018,"publication_date":"2018-06-23","ids":{"openalex":"https://openalex.org/W2625294292","doi":"https://doi.org/10.1007/s10898-018-0677-3","mag":"2625294292"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-018-0677-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-018-0677-3","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1706.04846","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Minh N. Dao","orcid":"https://orcid.org/0000-0002-8074-6675"},"institutions":[{"id":"https://openalex.org/I78757542","display_name":"University of Newcastle Australia","ror":"https://ror.org/00eae9z71","country_code":"AU","type":"education","lineage":["https://openalex.org/I78757542"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Minh N. Dao","raw_affiliation_strings":["CARMA, University of Newcastle, Callaghan, NSW, 2308, Australia"],"raw_orcid":"https://orcid.org/0000-0002-8074-6675","affiliations":[{"raw_affiliation_string":"CARMA, University of Newcastle, Callaghan, NSW, 2308, Australia","institution_ids":["https://openalex.org/I78757542"]}]},{"author_position":"last","author":{"id":null,"display_name":"Matthew K. Tam","orcid":null},"institutions":[{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthew K. Tam","raw_affiliation_strings":["Institut f\u00fcr Numerische und Angewandte Mathematik, Universit\u00e4t G\u00f6ttingen, 37083, G\u00f6ttingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Numerische und Angewandte Mathematik, Universit\u00e4t G\u00f6ttingen, 37083, G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I74656192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I78757542"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2780},"apc_paid":null,"fwci":3.206,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.92683657,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"73","issue":"1","first_page":"83","last_page":"112"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7958999872207642,"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":0.7958999872207642,"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":0.10649999976158142,"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":0.017400000244379044,"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/convexity","display_name":"Convexity","score":0.8173999786376953},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.739300012588501},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.7124999761581421},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.6384999752044678},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.49779999256134033},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4198000133037567},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.41839998960494995},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.38339999318122864},{"id":"https://openalex.org/keywords/symbolic-convergence-theory","display_name":"Symbolic convergence theory","score":0.3781999945640564}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8543000221252441},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.8173999786376953},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.739300012588501},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.7124999761581421},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.6384999752044678},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5020999908447266},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.49779999256134033},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4560999870300293},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4198000133037567},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.41839998960494995},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.38339999318122864},{"id":"https://openalex.org/C64980692","wikidata":"https://www.wikidata.org/wiki/Q16191959","display_name":"Symbolic convergence theory","level":3,"score":0.3781999945640564},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3375000059604645},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.3319999873638153},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.31929999589920044},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.3089999854564667},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.30480000376701355},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.2937000095844269},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.29269999265670776},{"id":"https://openalex.org/C89109886","wikidata":"https://www.wikidata.org/wiki/Q1535924","display_name":"Trust region","level":3,"score":0.2856000065803528},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C538505008","wikidata":"https://www.wikidata.org/wiki/Q3979448","display_name":"Convergence tests","level":4,"score":0.26030001044273376},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.25850000977516174},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10898-018-0677-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-018-0677-3","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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":"Journal of Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1706.04846","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.04846","pdf_url":"https://arxiv.org/pdf/1706.04846","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":"pmh:oai:RePEc:spr:jglopt:v:73:y:2019:i:1:d:10.1007_s10898-018-0677-3","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-018-0677-3","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1706.04846","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1706.04846","pdf_url":"https://arxiv.org/pdf/1706.04846","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/G4984910068","display_name":null,"funder_award_id":"RTG2088","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7504912770","display_name":null,"funder_award_id":"DP160101537","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W865342791","https://openalex.org/W1145378817","https://openalex.org/W1595803699","https://openalex.org/W1690193285","https://openalex.org/W1822348607","https://openalex.org/W1901524206","https://openalex.org/W1908403929","https://openalex.org/W1929806008","https://openalex.org/W1967317714","https://openalex.org/W1983380668","https://openalex.org/W2003372231","https://openalex.org/W2019569173","https://openalex.org/W2078394884","https://openalex.org/W2108078415","https://openalex.org/W2128475913","https://openalex.org/W2153562582","https://openalex.org/W2158902838","https://openalex.org/W2166406271","https://openalex.org/W2171505904","https://openalex.org/W2338282382","https://openalex.org/W2617461187","https://openalex.org/W2796899174","https://openalex.org/W2951407603","https://openalex.org/W2962916293","https://openalex.org/W2963847952","https://openalex.org/W2963899645","https://openalex.org/W4229650096","https://openalex.org/W4249513058"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2017-06-23T00:00:00"}
