{"id":"https://openalex.org/W4375860068","doi":"https://doi.org/10.1137/23n975703","title":"Education","display_name":"Education","publication_year":2023,"publication_date":"2023-05-01","ids":{"openalex":"https://openalex.org/W4375860068","doi":"https://doi.org/10.1137/23n975703"},"language":"en","primary_location":{"id":"doi:10.1137/23n975703","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/23n975703","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5034818712","display_name":"H\u00e9l\u00e8ne Frankowska","orcid":"https://orcid.org/0000-0001-6237-4137"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"H\u00e9l\u00e8ne Frankowska","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5034818712"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02358729,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"2","first_page":"537","last_page":"537"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.7736999988555908,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T11082","display_name":"Spacecraft Dynamics and Control","score":0.7736999988555908,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5812466740608215},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5644441246986389},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5358489751815796},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5269718170166016},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4844077229499817},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.47829777002334595},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4731289744377136},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4647125005722046},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.45236581563949585},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44698312878608704},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3747413158416748},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3592342138290405},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1287027895450592},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12139686942100525},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.07353949546813965}],"concepts":[{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5812466740608215},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5644441246986389},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5358489751815796},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5269718170166016},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4844077229499817},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.47829777002334595},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4731289744377136},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4647125005722046},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.45236581563949585},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44698312878608704},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3747413158416748},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3592342138290405},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1287027895450592},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12139686942100525},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.07353949546813965},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23n975703","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/23n975703","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4313177131","https://openalex.org/W2040676043","https://openalex.org/W1977643895","https://openalex.org/W2756132392","https://openalex.org/W3125145310","https://openalex.org/W2391091101","https://openalex.org/W3035814349","https://openalex.org/W2094599579","https://openalex.org/W2051968184","https://openalex.org/W2187449906"],"abstract_inverted_index":{"The":[0,80,113,191],"Education":[1],"section":[2],"in":[3,26,44,52,55,74,158,272,297,362,407],"this":[4,29,159,341,367,393],"issue":[5],"presents":[6],"two":[7,234,269],"contributions.":[8],"In":[9],"`\"Nesterov's":[10],"Method":[11],"for":[12,22,32,180,403],"Convex":[13],"Optimization,\"":[14],"Noel":[15],"J.":[16],"Walkington":[17],"proposes":[18],"a":[19,23,37,62,143,148,169,174,324,330,344,352,369],"teaching":[20],"guide":[21],"first":[24,42,92,114],"course":[25],"optimization":[27,54,181],"of":[28,36,58,82,90,98,131,142,168,176,197,215,218,332,347,359,372],"well-known":[30],"algorithm":[31,94,179],"computing":[33],"the":[34,56,67,83,121,132,136,140,177,213,216,219,236,263,280,294,348,357,360,363],"minimum":[35],"convex":[38,125,145,151,189],"function.":[39,152],"This":[40],"algorithm,":[41],"proposed":[43,106,329],"1983":[45],"by":[46,107,165,186,202,382],"Yuri":[47],"Nesterov,":[48],"though":[49],"well":[50],"recognized":[51],"computational":[53],"presence":[57],"large":[59],"data":[60],"as":[61],"more":[63],"efficient":[64],"tool":[65],"than":[66],"steepest":[68,99],"descent":[69,100],"method,":[70],"is":[71,200,375],"still":[72],"absent":[73,313],"most":[75],"modern":[76,315],"textbooks":[77],"on":[78,335,356],"optimization.":[79],"author":[81],"present":[84],"article":[85,342],"develops":[86],"an":[87,103,116,166],"elementary":[88],"analysis":[89],"Nesterov's":[91],"order":[93],"that":[95,97,238,255,274,277],"parallels":[96],"but":[101,300],"with":[102,183],"additional":[104],"requirement":[105],"Nesterov.":[108],"Two":[109],"cases":[110],"are":[111,156,162,232,242,257,279],"discussed.":[112],"concerns":[115,212],"unconstrained":[117],"minimization":[118],"problem,":[119],"while":[120],"second":[122,192],"includes":[123],"closed":[124],"constraints":[126,184],"represented":[127],"using":[128],"infinite":[129],"penalization":[130],"cost.":[133],"More":[134],"generally,":[135],"cost":[137],"function":[138,146],"becomes":[139],"sum":[141],"smooth":[144],"and":[147,173,208,223,246,392],"lower":[149],"semicontinuous":[150],"Several":[153],"student-level":[154],"exercises":[155],"included":[157],"paper.":[160],"Results":[161],"nicely":[163],"illustrated":[164],"example":[167],"signal":[170],"recovery":[171],"problem":[172,222],"discussion":[175],"Uzawa":[178],"problems":[182],"defined":[185],"inequalities":[187],"involving":[188],"functions.":[190],"paper,":[193],"\"A":[194],"Comprehensive":[195],"Proof":[196],"Bertrand's":[198,283,318,373],"Theorem,\"":[199],"presented":[201],"Patrick":[203],"De":[204],"Leenheer,":[205],"John":[206],"Musgrove,":[207],"Tyler":[209],"Schimleck.":[210],"It":[211],"behavior":[214],"solutions":[217],"classical":[220],"two-body":[221],"states":[224],"that,":[225],"among":[226],"all":[227,239],"possible":[228],"gravitational":[229,260],"laws,":[230],"there":[231,256],"only":[233,268,281],"exhibiting":[235],"property":[237],"bounded":[240],"orbits":[241],"closed:":[243],"Newtonian":[244],"gravitation":[245],"Hookean":[247],"gravitation.":[248],"Historically,":[249],"even":[250],"if":[251],"Newton":[252],"was":[253,267],"aware":[254],"to":[258,286,304,311,398],"specific":[259,353],"laws":[261],"having":[262],"above":[264],"property,":[265],"it":[266,333],"centuries":[270],"later,":[271],"1873,":[273],"Bertrand":[275],"realized":[276],"these":[278],"ones.":[282],"theorem,":[284],"due":[285],"its":[287,301],"important":[288],"consequences,":[289],"has":[290],"been":[291],"integrated":[292],"into":[293],"undergraduate":[295,305,405],"curriculum":[296],"theoretical":[298],"mechanics,":[299],"proof,":[302,326],"accessible":[303],"mathematics":[306,408],"or":[307,409],"physics":[308],"students,":[309],"seems":[310],"be":[312,396],"from":[314],"textbooks.":[316],"Although":[317],"original":[319],"paper":[320,394],"did":[321],"not":[322,388],"contain":[323],"precise":[325],"V.":[327],"Arnold":[328],"sketch":[331],"based":[334],"six":[336],"subproblems.":[337],"Among":[338],"other":[339,383],"contributions,":[340],"provides":[343],"complete":[345,370],"proof":[346,371],"sixth":[349],"subproblem":[350],"under":[351],"assumption":[354],"imposed":[355],"magnitude":[358],"force":[361],"motion":[364],"model.":[365],"Under":[366],"assumption,":[368],"theorem":[374],"then":[376],"given,":[377],"incorporating":[378],"also":[379],"earlier":[380],"contributions":[381],"authors.":[384],"Still,":[385],"comprehensive":[386],"does":[387],"mean":[389],"simple":[390],"here,":[391],"may":[395],"used":[397],"conceive":[399],"several":[400],"research":[401],"projects":[402],"advanced-level":[404],"students":[406],"physics.":[410]},"counts_by_year":[],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2023-05-10T00:00:00"}