{"id":"https://openalex.org/W2762269604","doi":"https://doi.org/10.1109/cdc.2017.8263743","title":"Local convergence of proximal splitting methods for rank constrained problems","display_name":"Local convergence of proximal splitting methods for rank constrained problems","publication_year":2017,"publication_date":"2017-12-01","ids":{"openalex":"https://openalex.org/W2762269604","doi":"https://doi.org/10.1109/cdc.2017.8263743","mag":"2762269604"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2017.8263743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2017.8263743","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1710.04248","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077723724","display_name":"Christian Gru\u00dfler","orcid":"https://orcid.org/0000-0003-2437-3154"},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Christian Grussler","raw_affiliation_strings":["Department of Automatic Control, Lund University, Lund, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, Lund University, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030031115","display_name":"Pontus Giselsson","orcid":"https://orcid.org/0000-0003-1602-1204"},"institutions":[{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Pontus Giselsson","raw_affiliation_strings":["Department of Automatic Control, Lund University, Lund, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Automatic Control, Lund University, Lund, Sweden","institution_ids":["https://openalex.org/I187531555"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I187531555"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"40","issue":null,"first_page":"702","last_page":"708"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9973000288009644,"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":0.9965000152587891,"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/rank","display_name":"Rank (graph theory)","score":0.636556088924408},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.631945013999939},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5657647848129272},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5623072385787964},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5575227737426758},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.551652729511261},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5508459210395813},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5391514897346497},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5383805632591248},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.5365092754364014},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5201371312141418},{"id":"https://openalex.org/keywords/proper-convex-function","display_name":"Proper convex function","score":0.4731924533843994},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.4540097117424011},{"id":"https://openalex.org/keywords/operator-splitting","display_name":"Operator splitting","score":0.4493747055530548},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.4207164943218231},{"id":"https://openalex.org/keywords/envelope","display_name":"Envelope (radar)","score":0.4124060273170471},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2966877222061157},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26329052448272705},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24879148602485657},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06782704591751099}],"concepts":[{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.636556088924408},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.631945013999939},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5657647848129272},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5623072385787964},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5575227737426758},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.551652729511261},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5508459210395813},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5391514897346497},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5383805632591248},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.5365092754364014},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5201371312141418},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.4731924533843994},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.4540097117424011},{"id":"https://openalex.org/C2987355758","wikidata":"https://www.wikidata.org/wiki/Q25037251","display_name":"Operator splitting","level":2,"score":0.4493747055530548},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.4207164943218231},{"id":"https://openalex.org/C65155139","wikidata":"https://www.wikidata.org/wiki/Q5380912","display_name":"Envelope (radar)","level":3,"score":0.4124060273170471},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2966877222061157},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26329052448272705},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24879148602485657},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06782704591751099},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/cdc.2017.8263743","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2017.8263743","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE 56th Annual Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1710.04248","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.04248","pdf_url":"https://arxiv.org/pdf/1710.04248","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:generic.eprints.org:963212","is_oa":false,"landing_page_url":"http://publications.eng.cam.ac.uk/963212/","pdf_url":null,"source":{"id":"https://openalex.org/S4406922847","display_name":"Cambridge University Engineering Department Publications Database","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Conference or Workshop Item"},{"id":"pmh:oai:lup.lub.lu.se:4f4acfd8-f8d8-4647-bb6b-f8ac2d5311f6","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/4f4acfd8-f8d8-4647-bb6b-f8ac2d5311f6","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"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":"info:eu-repo/semantics/conferencePaper"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1710.04248","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.04248","pdf_url":"https://arxiv.org/pdf/1710.04248","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W56210758","https://openalex.org/W83404773","https://openalex.org/W658559791","https://openalex.org/W1523985187","https://openalex.org/W1534416612","https://openalex.org/W1551480811","https://openalex.org/W1946620893","https://openalex.org/W2003372231","https://openalex.org/W2013243898","https://openalex.org/W2019569173","https://openalex.org/W2029213856","https://openalex.org/W2045079045","https://openalex.org/W2045286779","https://openalex.org/W2057122525","https://openalex.org/W2058532290","https://openalex.org/W2118550318","https://openalex.org/W2145096794","https://openalex.org/W2145486464","https://openalex.org/W2149934276","https://openalex.org/W2164278908","https://openalex.org/W2167077875","https://openalex.org/W2171505904","https://openalex.org/W2244987555","https://openalex.org/W2466668725","https://openalex.org/W2564702731","https://openalex.org/W2568451349","https://openalex.org/W2575226843","https://openalex.org/W3098387023","https://openalex.org/W3098812335","https://openalex.org/W3104665944","https://openalex.org/W3124617746","https://openalex.org/W4229650096","https://openalex.org/W4229706427","https://openalex.org/W4232936225","https://openalex.org/W4249667877","https://openalex.org/W4251038355","https://openalex.org/W4292363360","https://openalex.org/W6682162699"],"related_works":["https://openalex.org/W2026600343","https://openalex.org/W4382519084","https://openalex.org/W2356261519","https://openalex.org/W2478309485","https://openalex.org/W2040676043","https://openalex.org/W165488893","https://openalex.org/W1510770274","https://openalex.org/W4361807553","https://openalex.org/W1974461145","https://openalex.org/W2116973230"],"abstract_inverted_index":{"We":[0],"analyze":[1],"the":[2,27,34,41,56,69,77],"local":[3,50],"convergence":[4],"of":[5,30,44],"proximal":[6,28,42],"splitting":[7],"algorithms":[8,58],"to":[9,40,61,75],"solve":[10,76],"optimization":[11],"problems":[12],"that":[13,55],"are":[14],"convex":[15,46,66,70],"besides":[16],"a":[17,31,62,65],"rank":[18,35],"constraint.":[19],"For":[20],"this,":[21],"we":[22],"show":[23],"conditions":[24,53],"under":[25],"which":[26],"operator":[29,43],"function":[32],"involving":[33,68],"constraint":[36],"is":[37],"locally":[38,59],"identical":[39],"its":[45],"envelope,":[47],"hence":[48],"implying":[49],"convergence.":[51],"The":[52],"imply":[54],"non-convex":[57,78],"converge":[60],"solution":[63],"whenever":[64],"relaxation":[67],"envelope":[71],"can":[72],"be":[73],"expected":[74],"problem.":[79]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}