{"id":"https://openalex.org/W2604980966","doi":"https://doi.org/10.1109/tsp.2017.2709262","title":"Classification and Regression Using an Outer Approximation Projection-Gradient Method","display_name":"Classification and Regression Using an Outer Approximation Projection-Gradient Method","publication_year":2017,"publication_date":"2017-05-26","ids":{"openalex":"https://openalex.org/W2604980966","doi":"https://doi.org/10.1109/tsp.2017.2709262","mag":"2604980966"},"language":"en","primary_location":{"id":"doi:10.1109/tsp.2017.2709262","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2017.2709262","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","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/1506.02196","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5108556119","display_name":"Michel Barlaud","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Michel Barlaud","raw_affiliation_strings":["Universit\u00e9 C\u00f4te d\u2019Azur, CNRS, I3S, Sophia Antipolis, France","Universit\u00e9 C\u00f4te d'Azur, CNRS, I3S, Sophia Antipolis, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d\u2019Azur, CNRS, I3S, Sophia Antipolis, France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d'Azur, CNRS, I3S, Sophia Antipolis, France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044873015","display_name":"Wafa Belhajali","orcid":null},"institutions":[{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Wafa Belhajali","raw_affiliation_strings":["Universit\u00e9 C\u00f4te d\u2019Azur, CNRS, I3S, Sophia Antipolis, France","Universit\u00e9 C\u00f4te d'Azur, CNRS, I3S, Sophia Antipolis, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d\u2019Azur, CNRS, I3S, Sophia Antipolis, France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d'Azur, CNRS, I3S, Sophia Antipolis, France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081924048","display_name":"Patrick L. Combettes","orcid":"https://orcid.org/0000-0001-9730-5932"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patrick L. Combettes","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, Raleigh, NC, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045583054","display_name":"Lionel Fillatre","orcid":"https://orcid.org/0000-0002-8152-1769"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I201841394","display_name":"Universit\u00e9 C\u00f4te d'Azur","ror":"https://ror.org/019tgvf94","country_code":"FR","type":"education","lineage":["https://openalex.org/I201841394"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Lionel Fillatre","raw_affiliation_strings":["Universit\u00e9 C\u00f4te d\u2019Azur, CNRS, I3S, Sophia Antipolis, France","Universit\u00e9 C\u00f4te d'Azur, CNRS, I3S, Sophia Antipolis, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d\u2019Azur, CNRS, I3S, Sophia Antipolis, France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Universit\u00e9 C\u00f4te d'Azur, CNRS, I3S, Sophia Antipolis, France","institution_ids":["https://openalex.org/I201841394","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5108556119"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I201841394"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.03554678,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"65","issue":"17","first_page":"4635","last_page":"4644"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9994999766349792,"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":0.9994999766349792,"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/T10136","display_name":"Statistical Methods and Inference","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10308","display_name":"Systemic Lupus Erythematosus Research","score":0.9370999932289124,"subfield":{"id":"https://openalex.org/subfields/2745","display_name":"Rheumatology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6740022897720337},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5747821927070618},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.557674765586853},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5563849806785583},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5130154490470886},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.5071883201599121},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.4979081153869629},{"id":"https://openalex.org/keywords/subgradient-method","display_name":"Subgradient method","score":0.4938276708126068},{"id":"https://openalex.org/keywords/lasso","display_name":"Lasso (programming language)","score":0.47291502356529236},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.47289788722991943},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.461249977350235},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.44111761450767517},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.41189032793045044},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3796427249908447},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36294716596603394},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2214793860912323}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6740022897720337},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5747821927070618},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.557674765586853},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5563849806785583},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5130154490470886},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.5071883201599121},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.4979081153869629},{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.4938276708126068},{"id":"https://openalex.org/C37616216","wikidata":"https://www.wikidata.org/wiki/Q3218363","display_name":"Lasso (programming language)","level":2,"score":0.47291502356529236},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.47289788722991943},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.461249977350235},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.44111761450767517},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.41189032793045044},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3796427249908447},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36294716596603394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2214793860912323},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","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/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},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tsp.2017.2709262","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tsp.2017.2709262","pdf_url":null,"source":{"id":"https://openalex.org/S168680287","display_name":"IEEE Transactions on Signal Processing","issn_l":"1053-587X","issn":["1053-587X","1941-0476"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Signal Processing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1506.02196","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.02196","pdf_url":"https://arxiv.org/pdf/1506.02196","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:2604980966","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1506.02196.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":"doi:10.48550/arxiv.1506.02196","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1506.02196","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:1506.02196","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.02196","pdf_url":"https://arxiv.org/pdf/1506.02196","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.6700000166893005}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2604980966.pdf","grobid_xml":"https://content.openalex.org/works/W2604980966.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W205960364","https://openalex.org/W1506588750","https://openalex.org/W1569098853","https://openalex.org/W1618905105","https://openalex.org/W1886579186","https://openalex.org/W1946620893","https://openalex.org/W1966385142","https://openalex.org/W1967020502","https://openalex.org/W1970554427","https://openalex.org/W1978259121","https://openalex.org/W1993880409","https://openalex.org/W1997149618","https://openalex.org/W1999274908","https://openalex.org/W2006262045","https://openalex.org/W2012653948","https://openalex.org/W2013243898","https://openalex.org/W2015418199","https://openalex.org/W2021262032","https://openalex.org/W2033604629","https://openalex.org/W2062059813","https://openalex.org/W2092527476","https://openalex.org/W2097360283","https://openalex.org/W2100108897","https://openalex.org/W2107018762","https://openalex.org/W2107295961","https://openalex.org/W2108728387","https://openalex.org/W2116063398","https://openalex.org/W2118209906","https://openalex.org/W2119883478","https://openalex.org/W2122825543","https://openalex.org/W2125455772","https://openalex.org/W2129697675","https://openalex.org/W2133958955","https://openalex.org/W2135046866","https://openalex.org/W2140514146","https://openalex.org/W2143426320","https://openalex.org/W2144037063","https://openalex.org/W2145867192","https://openalex.org/W2148603752","https://openalex.org/W2154332973","https://openalex.org/W2154947819","https://openalex.org/W2155988523","https://openalex.org/W2160450758","https://openalex.org/W2172143581","https://openalex.org/W2180180824","https://openalex.org/W2418848710","https://openalex.org/W2952975724","https://openalex.org/W4294541781","https://openalex.org/W6679294143","https://openalex.org/W6679665003","https://openalex.org/W6685044387"],"related_works":["https://openalex.org/W2523521166","https://openalex.org/W2962963232","https://openalex.org/W3034489717","https://openalex.org/W2949572279","https://openalex.org/W2949283623","https://openalex.org/W2939782843","https://openalex.org/W2914786990","https://openalex.org/W2040649920","https://openalex.org/W2953067687","https://openalex.org/W2288097181","https://openalex.org/W1871180460","https://openalex.org/W2132054311","https://openalex.org/W3105279496","https://openalex.org/W2770362671","https://openalex.org/W2793425295","https://openalex.org/W2037312253","https://openalex.org/W2001125761","https://openalex.org/W1504194272","https://openalex.org/W2950109329","https://openalex.org/W3037110101"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3,181],"sparse":[4],"feature":[5],"selection":[6],"and":[7,11,84,114,188],"grouping":[8],"for":[9,174],"classification":[10,14],"regression.":[12],"The":[13,94,126],"or":[15,43,70],"regression":[16],"problems":[17],"under":[18],"consideration":[19],"consists":[20],"of":[21,96,101,128,153,158,161,165],"minimizing":[22],"a":[23,36,44,91,108,115,151,175],"convex":[24,155,178],"empirical":[25],"risk":[26],"function":[27],"subject":[28],"to":[29,74],"an":[30,139],"\u2113":[31,38,46],"<sup":[32,39,47],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[33,40,48],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1</sup>":[34,49],"constraint,":[35,42],"pairwise":[37,45],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">\u221e</sup>":[41],"constraint.":[50,125],"Existing":[51],"work,":[52],"such":[53],"as":[54],"the":[55,76,86,97,102,112,119,124,133,145,159,166,170],"Lasso":[56],"formulation,":[57],"has":[58],"focused":[59],"mainly":[60],"on":[61,111,185],"Lagrangian":[62],"penalty":[63,196],"approximations,":[64],"which":[65,106,144],"often":[66],"require":[67],"ad":[68],"hoc":[69],"computationally":[71],"expensive":[72],"procedures":[73],"determine":[75],"penalization":[77],"parameter.":[78],"We":[79],"depart":[80],"from":[81],"this":[82],"approach":[83,130],"address":[85],"constrained":[87],"problem":[88,180],"directly":[89],"via":[90,138],"splitting":[92],"method.":[93],"structure":[95],"method":[98,194],"is":[99,131,136,148,172],"that":[100,132,192],"classical":[103],"gradient-projection":[104],"algorithm,":[105],"alternates":[107],"gradient":[109],"step":[110,117,135],"objective":[113],"projection":[116,134],"onto":[118],"lower":[120],"level":[121],"set":[122,147],"modeling":[123],"novelty":[127],"our":[129,193],"implemented":[137],"outer":[140],"approximation":[141],"scheme":[142],"in":[143],"constraint":[146],"approximated":[149],"by":[150,169],"sequence":[152],"simple":[154],"sets":[156],"consisting":[157],"intersection":[160],"two":[162],"half-spaces.":[163],"Convergence":[164],"iterates":[167],"generated":[168],"algorithm":[171],"established":[173],"general":[176],"smooth":[177],"minimization":[179],"inequality":[182],"constraints.":[183],"Experiments":[184],"both":[186],"synthetic":[187],"biological":[189],"data":[190],"show":[191],"outperforms":[195],"methods.":[197]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
