{"id":"https://openalex.org/W2000656810","doi":"https://doi.org/10.1109/acc.2013.6580579","title":"Epoch gradient descent for smoothed hinge-loss linear SVMs","display_name":"Epoch gradient descent for smoothed hinge-loss linear SVMs","publication_year":2013,"publication_date":"2013-06-01","ids":{"openalex":"https://openalex.org/W2000656810","doi":"https://doi.org/10.1109/acc.2013.6580579","mag":"2000656810"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2013.6580579","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2013.6580579","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 American Control Conference","raw_type":"proceedings-article"},"type":"conference-paper","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/A5100734097","display_name":"Soomin Lee","orcid":"https://orcid.org/0000-0003-3959-6473"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Soomin Lee","raw_affiliation_strings":["Electrical and Computer Engineering, University of Illinois, Urbana, IL, USA","Electr. & Comput. Eng., Univ. of Illinois, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering, University of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Electr. & Comput. Eng., Univ. of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110629459","display_name":"Angelia Nedi\u0107","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Angelia Nedic","raw_affiliation_strings":["Faculty of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, IL, USA","Fac. of Ind. & Enterprise Syst. Eng., Univ. of Illinois, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Industrial and Enterprise Systems Engineering, University of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Fac. of Ind. & Enterprise Syst. Eng., Univ. of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"4789","last_page":"4794"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9950000047683716,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8395251035690308},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.7079166769981384},{"id":"https://openalex.org/keywords/hinge-loss","display_name":"Hinge loss","score":0.6581394672393799},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"Stochastic gradient descent","score":0.5932440757751465},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5915059447288513},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.5887224078178406},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.5840672850608826},{"id":"https://openalex.org/keywords/support-vector-machine","display_name":"Support vector machine","score":0.5726644396781921},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5675185918807983},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5386083126068115},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4713308811187744},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.4607786536216736},{"id":"https://openalex.org/keywords/margin","display_name":"Margin (machine learning)","score":0.41461181640625},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38903549313545227},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3835294842720032},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34118837118148804},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29228824377059937},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.22374042868614197},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12413311004638672},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.0957588255405426}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8395251035690308},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.7079166769981384},{"id":"https://openalex.org/C39891107","wikidata":"https://www.wikidata.org/wiki/Q5767098","display_name":"Hinge loss","level":3,"score":0.6581394672393799},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.5932440757751465},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5915059447288513},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.5887224078178406},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5840672850608826},{"id":"https://openalex.org/C12267149","wikidata":"https://www.wikidata.org/wiki/Q282453","display_name":"Support vector machine","level":2,"score":0.5726644396781921},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5675185918807983},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5386083126068115},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4713308811187744},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.4607786536216736},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.41461181640625},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38903549313545227},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3835294842720032},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34118837118148804},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29228824377059937},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.22374042868614197},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12413311004638672},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0957588255405426},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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":1,"locations":[{"id":"doi:10.1109/acc.2013.6580579","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2013.6580579","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1583497301","https://openalex.org/W1978259121","https://openalex.org/W2035720976","https://openalex.org/W2043182541","https://openalex.org/W2064575768","https://openalex.org/W2091825929","https://openalex.org/W2125993116","https://openalex.org/W2140214528","https://openalex.org/W2147898188","https://openalex.org/W2150621701","https://openalex.org/W2156909104","https://openalex.org/W2167732364","https://openalex.org/W6635018136","https://openalex.org/W6680443865"],"related_works":["https://openalex.org/W3197169288","https://openalex.org/W3177326532","https://openalex.org/W3143650729","https://openalex.org/W2042173174","https://openalex.org/W2744293077","https://openalex.org/W3128659392","https://openalex.org/W2082542187","https://openalex.org/W2355987247","https://openalex.org/W202635397","https://openalex.org/W2953360398"],"abstract_inverted_index":{"A":[0],"gradient":[1,60,69,107],"descent":[2],"method":[3,70],"for":[4],"strongly":[5,42],"convex":[6,43],"problems":[7],"with":[8,37,55],"Lipschitz":[9,49,58],"continuous":[10,50,59],"gradients":[11],"requires":[12],"only":[13],"O(log":[14],"<sub":[15],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[16],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</sub>":[17],"\u03b5)":[18],"iterations":[19],"to":[20],"obtain":[21,91],"an":[22,92],"\u03b5-accurate":[23],"solution":[24,81],"(q":[25],"is":[26,82],"a":[27,98,103],"constant":[28],"in":[29],"(0;":[30],"1)).":[31],"Support":[32],"Vector":[33],"Machines":[34],"(SVMs)":[35],"penalized":[36],"the":[38,73,79,84],"popular":[39],"hinge-loss":[40],"are":[41],"but":[44,78],"they":[45],"do":[46],"not":[47,83],"have":[48],"gradient.":[51],"We":[52],"find":[53],"SVMs":[54],"strong-convexity":[56],"and":[57],"using":[61],"Nesterov's":[62],"smooth":[63],"approximation":[64],"technique":[65],"[1].":[66],"The":[67],"simple":[68],"applied":[71],"on":[72],"smoothed":[74],"SVM":[75],"converges":[76],"fast":[77,99],"obtained":[80],"exact":[85,93],"maximum":[86],"margin":[87],"separating":[88],"hyperplane.":[89],"To":[90],"solution,":[94],"as":[95,97],"well":[96],"convergence,":[100],"we":[101],"propose":[102],"hybrid":[104],"approach,":[105],"epoch":[106],"descent.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}