{"id":"https://openalex.org/W2997964792","doi":"https://doi.org/10.1146/annurev-control-091819-074326","title":"Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics","display_name":"Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics","publication_year":2019,"publication_date":"2019-12-24","ids":{"openalex":"https://openalex.org/W2997964792","doi":"https://doi.org/10.1146/annurev-control-091819-074326","mag":"2997964792"},"language":"en","primary_location":{"id":"doi:10.1146/annurev-control-091819-074326","is_oa":true,"landing_page_url":"https://doi.org/10.1146/annurev-control-091819-074326","pdf_url":"https://www.annualreviews.org/doi/pdf/10.1146/annurev-control-091819-074326","source":{"id":"https://openalex.org/S4210191328","display_name":"Annual Review of Control Robotics and Autonomous Systems","issn_l":"2573-5144","issn":["2573-5144"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320373","host_organization_name":"Annual Reviews","host_organization_lineage":["https://openalex.org/P4310320373"],"host_organization_lineage_names":["Annual Reviews"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annual Review of Control, Robotics, and Autonomous Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.annualreviews.org/doi/pdf/10.1146/annurev-control-091819-074326","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013839863","display_name":"Anirudha Majumdar","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anirudha Majumdar","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA;","institution_ids":["https://openalex.org/I20089843"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088502139","display_name":"Georgina Hall","orcid":"https://orcid.org/0000-0003-4580-3897"},"institutions":[{"id":"https://openalex.org/I102272798","display_name":"INSEAD","ror":"https://ror.org/00ghzk478","country_code":"FR","type":"education","lineage":["https://openalex.org/I102272798"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Georgina Hall","raw_affiliation_strings":["Decision Sciences, INSEAD, 77300 Fontainebleau, France;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Decision Sciences, INSEAD, 77300 Fontainebleau, France;","institution_ids":["https://openalex.org/I102272798"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101485690","display_name":"Amir Ali Ahmadi","orcid":"https://orcid.org/0009-0001-5743-354X"},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Amir Ali Ahmadi","raw_affiliation_strings":["Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544, USA;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544, USA;","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.2215,"has_fulltext":true,"cited_by_count":90,"citation_normalized_percentile":{"value":0.98915898,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"3","issue":"1","first_page":"331","last_page":"360"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9961000084877014,"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":0.9959999918937683,"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/semidefinite-programming","display_name":"Semidefinite programming","score":0.809046745300293},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.7378647327423096},{"id":"https://openalex.org/keywords/robotics","display_name":"Robotics","score":0.6339783072471619},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6207432746887207},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.613203763961792},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.5474109053611755},{"id":"https://openalex.org/keywords/exploit","display_name":"Exploit","score":0.42708003520965576},{"id":"https://openalex.org/keywords/semidefinite-embedding","display_name":"Semidefinite embedding","score":0.41074681282043457},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3223830461502075},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.28123462200164795},{"id":"https://openalex.org/keywords/robot","display_name":"Robot","score":0.23459875583648682},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1779584288597107},{"id":"https://openalex.org/keywords/quadratically-constrained-quadratic-program","display_name":"Quadratically constrained quadratic program","score":0.16828912496566772},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.15204784274101257}],"concepts":[{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.809046745300293},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.7378647327423096},{"id":"https://openalex.org/C34413123","wikidata":"https://www.wikidata.org/wiki/Q170978","display_name":"Robotics","level":3,"score":0.6339783072471619},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6207432746887207},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.613203763961792},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5474109053611755},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.42708003520965576},{"id":"https://openalex.org/C206818286","wikidata":"https://www.wikidata.org/wiki/Q7449403","display_name":"Semidefinite embedding","level":4,"score":0.41074681282043457},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3223830461502075},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28123462200164795},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.23459875583648682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1779584288597107},{"id":"https://openalex.org/C65148998","wikidata":"https://www.wikidata.org/wiki/Q7268373","display_name":"Quadratically constrained quadratic program","level":3,"score":0.16828912496566772},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.15204784274101257},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1146/annurev-control-091819-074326","is_oa":true,"landing_page_url":"https://doi.org/10.1146/annurev-control-091819-074326","pdf_url":"https://www.annualreviews.org/doi/pdf/10.1146/annurev-control-091819-074326","source":{"id":"https://openalex.org/S4210191328","display_name":"Annual Review of Control Robotics and Autonomous Systems","issn_l":"2573-5144","issn":["2573-5144"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320373","host_organization_name":"Annual Reviews","host_organization_lineage":["https://openalex.org/P4310320373"],"host_organization_lineage_names":["Annual Reviews"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annual Review of Control, Robotics, and Autonomous Systems","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1146/annurev-control-091819-074326","is_oa":true,"landing_page_url":"https://doi.org/10.1146/annurev-control-091819-074326","pdf_url":"https://www.annualreviews.org/doi/pdf/10.1146/annurev-control-091819-074326","source":{"id":"https://openalex.org/S4210191328","display_name":"Annual Review of Control Robotics and Autonomous Systems","issn_l":"2573-5144","issn":["2573-5144"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320373","host_organization_name":"Annual Reviews","host_organization_lineage":["https://openalex.org/P4310320373"],"host_organization_lineage_names":["Annual Reviews"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annual Review of Control, Robotics, and Autonomous Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320332815","display_name":"Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2997964792.pdf","grobid_xml":"https://content.openalex.org/works/W2997964792.grobid-xml"},"referenced_works_count":105,"referenced_works":["https://openalex.org/W1024110","https://openalex.org/W431400460","https://openalex.org/W653291882","https://openalex.org/W1486132939","https://openalex.org/W1540529426","https://openalex.org/W1775587472","https://openalex.org/W1822269556","https://openalex.org/W1833752784","https://openalex.org/W1861508522","https://openalex.org/W1918816242","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1979463193","https://openalex.org/W1985123706","https://openalex.org/W1986219860","https://openalex.org/W1986699627","https://openalex.org/W2000998728","https://openalex.org/W2004902288","https://openalex.org/W2005102197","https://openalex.org/W2006704773","https://openalex.org/W2014495508","https://openalex.org/W2030686911","https://openalex.org/W2034769312","https://openalex.org/W2035412546","https://openalex.org/W2047071281","https://openalex.org/W2049371785","https://openalex.org/W2051434435","https://openalex.org/W2055993677","https://openalex.org/W2065110770","https://openalex.org/W2071143636","https://openalex.org/W2071410137","https://openalex.org/W2078289947","https://openalex.org/W2080359169","https://openalex.org/W2080795645","https://openalex.org/W2084148362","https://openalex.org/W2088369373","https://openalex.org/W2093875902","https://openalex.org/W2099799470","https://openalex.org/W2110662303","https://openalex.org/W2111826413","https://openalex.org/W2117198760","https://openalex.org/W2118550318","https://openalex.org/W2122796095","https://openalex.org/W2124487034","https://openalex.org/W2126746199","https://openalex.org/W2133404041","https://openalex.org/W2135779729","https://openalex.org/W2136885855","https://openalex.org/W2138505091","https://openalex.org/W2143075842","https://openalex.org/W2145139206","https://openalex.org/W2145962650","https://openalex.org/W2166161233","https://openalex.org/W2170975529","https://openalex.org/W2180077832","https://openalex.org/W2180612164","https://openalex.org/W2194838607","https://openalex.org/W2255205876","https://openalex.org/W2272603263","https://openalex.org/W2283023501","https://openalex.org/W2288174618","https://openalex.org/W2290522125","https://openalex.org/W2290808543","https://openalex.org/W2292758822","https://openalex.org/W2336416123","https://openalex.org/W2342045095","https://openalex.org/W2402588523","https://openalex.org/W2408654640","https://openalex.org/W2490900388","https://openalex.org/W2536620281","https://openalex.org/W2543927648","https://openalex.org/W2547811925","https://openalex.org/W2559655401","https://openalex.org/W2568443424","https://openalex.org/W2568585091","https://openalex.org/W2593062745","https://openalex.org/W2604272474","https://openalex.org/W2615253071","https://openalex.org/W2734507298","https://openalex.org/W2738121580","https://openalex.org/W2765212321","https://openalex.org/W2794029565","https://openalex.org/W2795405496","https://openalex.org/W2809630376","https://openalex.org/W2912522929","https://openalex.org/W2963326979","https://openalex.org/W2963566960","https://openalex.org/W2963663060","https://openalex.org/W2967247330","https://openalex.org/W2967626315","https://openalex.org/W2999905431","https://openalex.org/W3100916622","https://openalex.org/W3101302494","https://openalex.org/W3105558219","https://openalex.org/W3105686649","https://openalex.org/W3106518847","https://openalex.org/W3113425034","https://openalex.org/W3117881175","https://openalex.org/W3124734834","https://openalex.org/W4205169475","https://openalex.org/W4205293427","https://openalex.org/W4212764898","https://openalex.org/W4255442211","https://openalex.org/W4292363360","https://openalex.org/W4296926842"],"related_works":["https://openalex.org/W2385886188","https://openalex.org/W2288891047","https://openalex.org/W2524928742","https://openalex.org/W2362452378","https://openalex.org/W2353517195","https://openalex.org/W3166939022","https://openalex.org/W1727084346","https://openalex.org/W2544939111","https://openalex.org/W2386048074","https://openalex.org/W2572095861"],"abstract_inverted_index":{"Historically,":[0],"scalability":[1,77],"has":[2],"been":[3],"a":[4,43,98,120,144],"major":[5],"challenge":[6],"for":[7,156],"the":[8,67,105,129,133,147],"successful":[9],"application":[10],"of":[11,70,94,122,128],"semidefinite":[12,52,83,154],"programming":[13,155],"in":[14,42,132],"fields":[15],"such":[16],"as":[17,143],"machine":[18,112],"learning,":[19,113],"control,":[20,114],"and":[21,40,66,72,87,108,149,159],"robotics.":[22,116],"In":[23],"this":[24,31,139],"article,":[25],"we":[26,96],"survey":[27],"recent":[28],"approaches":[29],"to":[30,51,104,146],"challenge,":[32],"including":[33],"those":[34,45,54,73],"that":[35,46,55,60,74,125,138],"exploit":[36],"structure":[37],"(e.g.,":[38,80],"sparsity":[39],"symmetry)":[41],"problem,":[44],"produce":[47],"low-rank":[48],"approximate":[49],"solutions":[50],"programs,":[53],"use":[56],"more":[57],"scalable":[58,153],"algorithms":[59],"rely":[61],"on":[62,152],"augmented":[63],"Lagrangian":[64],"techniques":[65,130],"alternating-direction":[68],"method":[69],"multipliers,":[71],"trade":[75],"off":[76],"with":[78,85],"conservatism":[79],"by":[81],"approximating":[82],"programs":[84],"linear":[86],"second-order":[88],"cone":[89],"programs).":[90],"For":[91],"each":[92],"class":[93],"approaches,":[95],"provide":[97],"high-level":[99],"exposition,":[100],"an":[101],"entry":[102],"point":[103],"corresponding":[106],"literature,":[107],"examples":[109],"drawn":[110],"from":[111],"or":[115],"We":[117],"also":[118],"present":[119],"list":[121],"software":[123],"packages":[124],"implement":[126],"many":[127],"discussed":[131],"review.":[134],"Our":[135],"hope":[136],"is":[137],"article":[140],"will":[141],"serve":[142],"gateway":[145],"rich":[148],"exciting":[150],"literature":[151],"both":[157],"theorists":[158],"practitioners.":[160]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":22},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}