{"id":"https://openalex.org/W2966922517","doi":"https://doi.org/10.23919/ecc.2019.8796148","title":"Random gradient algorithms for convex minimization over intersection of simple sets","display_name":"Random gradient algorithms for convex minimization over intersection of simple sets","publication_year":2019,"publication_date":"2019-06-01","ids":{"openalex":"https://openalex.org/W2966922517","doi":"https://doi.org/10.23919/ecc.2019.8796148","mag":"2966922517"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2019.8796148","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2019.8796148","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 18th European Control Conference (ECC)","raw_type":"proceedings-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/A5019114471","display_name":"Ion Necoara","orcid":"https://orcid.org/0000-0003-1102-2654"},"institutions":[{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Ion Necoara","raw_affiliation_strings":["Automatic Control and Systems Engineering Department, University Politehnica Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Automatic Control and Systems Engineering Department, University Politehnica Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019114471"],"corresponding_institution_ids":["https://openalex.org/I61641377"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"993","last_page":"998"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9997000098228455,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991999864578247,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.987500011920929,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6278368830680847},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5541530847549438},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5494012236595154},{"id":"https://openalex.org/keywords/sublinear-function","display_name":"Sublinear function","score":0.5417661070823669},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5152390599250793},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.5152357220649719},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5039052367210388},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4907432794570923},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.47130832076072693},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4651765525341034},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.46154481172561646},{"id":"https://openalex.org/keywords/feasible-region","display_name":"Feasible region","score":0.45884546637535095},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4433937668800354},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4150792062282562},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38577455282211304},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3101707696914673},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.13447800278663635}],"concepts":[{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6278368830680847},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5541530847549438},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5494012236595154},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.5417661070823669},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5152390599250793},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5152357220649719},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5039052367210388},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4907432794570923},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.47130832076072693},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4651765525341034},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.46154481172561646},{"id":"https://openalex.org/C177067428","wikidata":"https://www.wikidata.org/wiki/Q17013331","display_name":"Feasible region","level":2,"score":0.45884546637535095},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4433937668800354},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4150792062282562},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38577455282211304},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3101707696914673},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.13447800278663635},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2019.8796148","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2019.8796148","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 18th European Control Conference (ECC)","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":32,"referenced_works":["https://openalex.org/W905619","https://openalex.org/W1859634276","https://openalex.org/W1976376589","https://openalex.org/W1981832695","https://openalex.org/W1992208280","https://openalex.org/W2012180727","https://openalex.org/W2033511209","https://openalex.org/W2124541940","https://openalex.org/W2131247345","https://openalex.org/W2148603752","https://openalex.org/W2156779765","https://openalex.org/W2166524953","https://openalex.org/W2339131702","https://openalex.org/W2398206539","https://openalex.org/W2521431955","https://openalex.org/W2695988161","https://openalex.org/W2793381907","https://openalex.org/W2963000588","https://openalex.org/W2963183767","https://openalex.org/W2963747836","https://openalex.org/W2963830980","https://openalex.org/W2963914745","https://openalex.org/W3096194929","https://openalex.org/W3097096317","https://openalex.org/W3141595720","https://openalex.org/W4205339158","https://openalex.org/W4297796973","https://openalex.org/W6600043445","https://openalex.org/W6688511951","https://openalex.org/W6691935205","https://openalex.org/W6739674677","https://openalex.org/W6784537261"],"related_works":["https://openalex.org/W2149119057","https://openalex.org/W2804400349","https://openalex.org/W4297153560","https://openalex.org/W2043851096","https://openalex.org/W2964186284","https://openalex.org/W2058485202","https://openalex.org/W3208916810","https://openalex.org/W4224283687","https://openalex.org/W4287828482","https://openalex.org/W4292651679"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,45,54],"consider":[4],"constrained":[5,130],"convex":[6,22,151],"optimization":[7,118],"problems,":[8],"where":[9,87],"the":[10,15,27,36,61,67,72,88,135,139,143,146,168,173,176,198],"constraints":[11],"are":[12,114],"described":[13],"as":[14,106,128],"intersection":[16,28],"of":[17,21,26,115,125,138,172,200],"a":[18,56,75,121,163],"finite":[19],"number":[20,124],"sets.":[23],"Each":[24],"set":[25,69,91,178],"is":[29,35,53,92,99,149],"assumed":[30],"to":[31,186],"be":[32,39],"simple,":[33],"that":[34,52],"projection":[37,73],"can":[38,82],"computed":[40],"efficiently.":[41],"For":[42],"these":[43,112],"problems":[44,119],"derive":[46],"gradient":[47,57],"methods":[48,202],"with":[49,153],"random":[50,76],"projections,":[51],"perform":[55],"step":[58],"for":[59,117,142,167,179,192],"minimizing":[60],"objective":[62,147],"function":[63,148],"and":[64,152],"then":[65],"access":[66],"feasible":[68,90],"only":[70],"through":[71,104],"onto":[74],"individual":[77],"set.":[78],"Thus,":[79],"our":[80,183,201],"algorithms":[81,113,141],"easily":[83],"address":[84],"streaming":[85],"settings,":[86],"whole":[89],"not":[93],"known":[94],"in":[95,102,107,129,203],"advance,":[96],"but":[97],"it":[98],"rather":[100],"learned":[101],"time":[103],"observations,":[105],"machine":[108],"learning":[109],"applications.":[110],"Also,":[111],"interest":[116],"having":[120],"very":[122],"large":[123],"given":[126],"constraints,":[127],"predictive":[131],"control.":[132],"We":[133,157],"analyze":[134],"convergence":[136,160],"behavior":[137],"proposed":[140],"case":[144],"when":[145],"strongly":[150],"Lipschitz":[154],"continuous":[155],"gradients.":[156],"prove":[158],"linear":[159],"rate":[161],"into":[162],"noise":[164],"dominated":[165],"region":[166],"expected":[169],"quadratic":[170],"distance":[171],"iterates":[174],"from":[175],"optimal":[177],"constant":[180],"stepsize.":[181,194],"However,":[182],"analysis":[184],"allows":[185],"also":[187],"provide":[188],"global":[189],"sublinear":[190],"rates":[191],"diminishing":[193],"Numerical":[195],"evidence":[196],"supports":[197],"effectiveness":[199],"real-world":[204],"problems.":[205]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
