{"id":"https://openalex.org/W2056145308","doi":"https://doi.org/10.1137/110853996","title":"Hankel Matrix Rank Minimization with Applications to System Identification and Realization","display_name":"Hankel Matrix Rank Minimization with Applications to System Identification and Realization","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2056145308","doi":"https://doi.org/10.1137/110853996","mag":"2056145308"},"language":"en","primary_location":{"id":"doi:10.1137/110853996","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110853996","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","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/A5102886973","display_name":"Maryam Fazel","orcid":"https://orcid.org/0000-0001-5329-4522"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Maryam Fazel","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065214298","display_name":"Ting Kei Pong","orcid":"https://orcid.org/0000-0001-5862-2986"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ting Kei Pong","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029911976","display_name":"Defeng Sun","orcid":"https://orcid.org/0000-0003-0481-272X"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Defeng Sun","raw_affiliation_strings":["National University of Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110258450","display_name":"Paul Tseng","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Tseng","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":36.682,"has_fulltext":false,"cited_by_count":507,"citation_normalized_percentile":{"value":0.99916669,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"34","issue":"3","first_page":"946","last_page":"977"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9968000054359436,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9912999868392944,"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/hankel-matrix","display_name":"Hankel matrix","score":0.7307165861129761},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.6695080995559692},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5998092889785767},{"id":"https://openalex.org/keywords/realization","display_name":"Realization (probability)","score":0.5205110907554626},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5140843987464905},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4736272692680359},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.4644733667373657},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4590339660644531},{"id":"https://openalex.org/keywords/matrix-norm","display_name":"Matrix norm","score":0.4478062093257904},{"id":"https://openalex.org/keywords/system-identification","display_name":"System identification","score":0.44354701042175293},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.42253977060317993},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.41366496682167053},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3134864866733551},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12174639105796814},{"id":"https://openalex.org/keywords/data-modeling","display_name":"Data modeling","score":0.09132605791091919}],"concepts":[{"id":"https://openalex.org/C25023664","wikidata":"https://www.wikidata.org/wiki/Q1575637","display_name":"Hankel matrix","level":2,"score":0.7307165861129761},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.6695080995559692},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5998092889785767},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.5205110907554626},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5140843987464905},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4736272692680359},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.4644733667373657},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4590339660644531},{"id":"https://openalex.org/C92207270","wikidata":"https://www.wikidata.org/wiki/Q939253","display_name":"Matrix norm","level":3,"score":0.4478062093257904},{"id":"https://openalex.org/C119247159","wikidata":"https://www.wikidata.org/wiki/Q1366192","display_name":"System identification","level":3,"score":0.44354701042175293},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.42253977060317993},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.41366496682167053},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3134864866733551},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12174639105796814},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.09132605791091919},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/110853996","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110853996","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/103363","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/103363","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"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":"Scopus","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.231.5341","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.231.5341","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.nus.edu.sg/%7Ematsundf/Hankelrm9.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.278.5726","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.278.5726","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.nus.edu.sg/%7Ematsundf/Hankelrm23.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.365.1242","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.365.1242","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://faculty.washington.edu/mfazel/Hankelrm23.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W182881619","https://openalex.org/W955428205","https://openalex.org/W1484739396","https://openalex.org/W1499670810","https://openalex.org/W1509803206","https://openalex.org/W1512958137","https://openalex.org/W1524324710","https://openalex.org/W1573301526","https://openalex.org/W1603765807","https://openalex.org/W1916337001","https://openalex.org/W1965324089","https://openalex.org/W1966096622","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1994147271","https://openalex.org/W2000157792","https://openalex.org/W2000955051","https://openalex.org/W2007437396","https://openalex.org/W2011359124","https://openalex.org/W2016910236","https://openalex.org/W2026517977","https://openalex.org/W2043275203","https://openalex.org/W2045079045","https://openalex.org/W2045704273","https://openalex.org/W2047071281","https://openalex.org/W2058532290","https://openalex.org/W2059283452","https://openalex.org/W2064431362","https://openalex.org/W2065030431","https://openalex.org/W2072536590","https://openalex.org/W2074471762","https://openalex.org/W2079365071","https://openalex.org/W2086325670","https://openalex.org/W2097883065","https://openalex.org/W2101868363","https://openalex.org/W2103972604","https://openalex.org/W2109161029","https://openalex.org/W2115727068","https://openalex.org/W2118550318","https://openalex.org/W2118682956","https://openalex.org/W2132346118","https://openalex.org/W2135631911","https://openalex.org/W2141601259","https://openalex.org/W2144730813","https://openalex.org/W2147523783","https://openalex.org/W2158923808","https://openalex.org/W2159405849","https://openalex.org/W2162451874","https://openalex.org/W2165281529","https://openalex.org/W2167732364","https://openalex.org/W2339666411","https://openalex.org/W2466299320","https://openalex.org/W2540877599","https://openalex.org/W2611328865","https://openalex.org/W2798909945","https://openalex.org/W2949483514","https://openalex.org/W3141595720","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2949966822","https://openalex.org/W4386863313","https://openalex.org/W1986851914","https://openalex.org/W2583841453","https://openalex.org/W2229973481","https://openalex.org/W2009353134","https://openalex.org/W2086669233","https://openalex.org/W2766262910","https://openalex.org/W2201692517","https://openalex.org/W2045714585"],"abstract_inverted_index":{"We":[0,30,54,141],"introduce":[1],"a":[2,127],"flexible":[3],"optimization":[4,39],"framework":[5],"for":[6,35,105,113],"nuclear":[7],"norm":[8],"minimization":[9],"of":[10,45,96,122,138,146,152],"matrices":[11],"with":[12],"linear":[13],"structure,":[14],"including":[15,41],"Hankel,":[16],"Toeplitz,":[17],"and":[18,21,50,66,84,102,107],"moment":[19],"structures":[20],"catalog":[22],"applications":[23],"from":[24],"diverse":[25],"fields":[26],"under":[27],"this":[28,156],"framework.":[29],"discuss":[31],"various":[32],"first-order":[33,92,134],"methods":[34,44,61,93,135,151],"solving":[36],"the":[37,71,75,85,114,118,144,147],"resulting":[38],"problem,":[40,74,117],"alternating":[42,119,149],"direction":[43,120,150],"multipliers,":[46,123],"proximal":[47,86,148],"point":[48,87],"algorithms,":[49],"gradient":[51,76],"projection":[52,77],"methods.":[53],"perform":[55],"computational":[56],"experiments":[57],"to":[58,126],"compare":[59],"these":[60],"on":[62,99],"system":[63,67,72,115],"identification":[64,73],"problems":[65],"realization":[68,116],"problems.":[69],"For":[70],"method":[78,121],"(accelerated":[79],"by":[80],"Nesterov's":[81],"extrapolation":[82],"techniques)":[83],"algorithm":[88],"usually":[89,131],"outperform":[90],"other":[91,133],"in":[94,136,155],"terms":[95,137],"CPU":[97,139],"time":[98],"both":[100],"real":[101],"simulated":[103],"data,":[104],"small":[106],"large":[108],"regularization":[109],"parameters,":[110],"respectively,":[111],"while":[112],"as":[124],"applied":[125],"certain":[128],"primal":[129],"reformulation,":[130],"outperforms":[132],"time.":[140],"also":[142],"study":[143],"convergence":[145],"multipliers":[153],"used":[154],"paper.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":26},{"year":2024,"cited_by_count":29},{"year":2023,"cited_by_count":36},{"year":2022,"cited_by_count":34},{"year":2021,"cited_by_count":49},{"year":2020,"cited_by_count":58},{"year":2019,"cited_by_count":54},{"year":2018,"cited_by_count":56},{"year":2017,"cited_by_count":42},{"year":2016,"cited_by_count":35},{"year":2015,"cited_by_count":39},{"year":2014,"cited_by_count":20},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":8}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}
