{"id":"https://openalex.org/W3097237335","doi":"https://doi.org/10.1109/tac.2021.3137147","title":"On the Absence of Spurious Local Trajectories in Time-Varying Nonconvex Optimization","display_name":"On the Absence of Spurious Local Trajectories in Time-Varying Nonconvex Optimization","publication_year":2021,"publication_date":"2021-12-21","ids":{"openalex":"https://openalex.org/W3097237335","doi":"https://doi.org/10.1109/tac.2021.3137147","mag":"3097237335"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3137147","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3137147","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","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/A5061966752","display_name":"Salar Fattahi","orcid":"https://orcid.org/0000-0001-7986-3148"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Salar Fattahi","raw_affiliation_strings":["University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":"https://orcid.org/0000-0001-7986-3148","affiliations":[{"raw_affiliation_string":"University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011573814","display_name":"C\u00e9dric Josz","orcid":"https://orcid.org/0000-0003-2882-8697"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cedric Josz","raw_affiliation_strings":["Columbia University, New York, NY, USA"],"raw_orcid":"https://orcid.org/0000-0003-2882-8697","affiliations":[{"raw_affiliation_string":"Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102879163","display_name":"Yuhao Ding","orcid":"https://orcid.org/0000-0002-1521-7566"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuhao Ding","raw_affiliation_strings":["University of California, Berkeley, Berkeley, CA, USA"],"raw_orcid":"https://orcid.org/0000-0002-1521-7566","affiliations":[{"raw_affiliation_string":"University of California, Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112854802","display_name":"Reza Mohammadi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210108346","display_name":"BioSensics (United States)","ror":"https://ror.org/01s2ng935","country_code":"US","type":"company","lineage":["https://openalex.org/I4210108346"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Reza Mohammadi","raw_affiliation_strings":["BioSensics, Newton, MA, USA"],"raw_orcid":"https://orcid.org/0000-0001-7494-3050","affiliations":[{"raw_affiliation_string":"BioSensics, Newton, MA, USA","institution_ids":["https://openalex.org/I4210108346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042580848","display_name":"Javad Lavaei","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Javad Lavaei","raw_affiliation_strings":["University of California, Berkeley, Berkeley, CA, USA"],"raw_orcid":"https://orcid.org/0000-0003-4294-1338","affiliations":[{"raw_affiliation_string":"University of California, Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072786751","display_name":"Somayeh Sojoudi","orcid":"https://orcid.org/0000-0001-7177-7712"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Somayeh Sojoudi","raw_affiliation_strings":["University of California, Berkeley, Berkeley, CA, USA"],"raw_orcid":"https://orcid.org/0000-0001-7177-7712","affiliations":[{"raw_affiliation_string":"University of California, Berkeley, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3038,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55968645,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"68","issue":"1","first_page":"80","last_page":"95"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12101","display_name":"Advanced Bandit Algorithms Research","score":0.9753999710083008,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.8530733585357666},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.7964409589767456},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.7174302339553833},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6971023082733154},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6396826505661011},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.561493992805481},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5431692600250244},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5275694131851196},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.5064185857772827},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46838313341140747},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.44157588481903076},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.439120352268219},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3314670920372009},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3160187602043152},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.24566900730133057},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.24534592032432556},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08901071548461914},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.08342400193214417}],"concepts":[{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.8530733585357666},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.7964409589767456},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.7174302339553833},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6971023082733154},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6396826505661011},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.561493992805481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5431692600250244},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5275694131851196},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5064185857772827},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46838313341140747},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.44157588481903076},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.439120352268219},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3314670920372009},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3160187602043152},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.24566900730133057},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.24534592032432556},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08901071548461914},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.08342400193214417},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2021.3137147","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3137147","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/1","score":0.6899999976158142,"display_name":"No poverty"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320335353","display_name":"National Science Foundation of Sri Lanka","ror":"https://ror.org/010xaa060"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":105,"referenced_works":["https://openalex.org/W240029891","https://openalex.org/W1518854728","https://openalex.org/W1526075880","https://openalex.org/W1543750907","https://openalex.org/W1580798812","https://openalex.org/W1594563152","https://openalex.org/W1823937713","https://openalex.org/W1976086748","https://openalex.org/W1992129985","https://openalex.org/W2007562422","https://openalex.org/W2009668633","https://openalex.org/W2013691830","https://openalex.org/W2039353469","https://openalex.org/W2043183450","https://openalex.org/W2047071281","https://openalex.org/W2050834445","https://openalex.org/W2055954415","https://openalex.org/W2059313737","https://openalex.org/W2067265108","https://openalex.org/W2082114857","https://openalex.org/W2093909370","https://openalex.org/W2097415784","https://openalex.org/W2098501540","https://openalex.org/W2098754650","https://openalex.org/W2106129230","https://openalex.org/W2123871098","https://openalex.org/W2124450277","https://openalex.org/W2134889984","https://openalex.org/W2141380252","https://openalex.org/W2162211921","https://openalex.org/W2186734734","https://openalex.org/W2266946488","https://openalex.org/W2276071760","https://openalex.org/W2358698356","https://openalex.org/W2374425248","https://openalex.org/W2405479119","https://openalex.org/W2467441529","https://openalex.org/W2474090883","https://openalex.org/W2485166818","https://openalex.org/W2528062157","https://openalex.org/W2547949325","https://openalex.org/W2592651140","https://openalex.org/W2601846890","https://openalex.org/W2604130501","https://openalex.org/W2611328865","https://openalex.org/W2616333561","https://openalex.org/W2751905567","https://openalex.org/W2777662428","https://openalex.org/W2791099456","https://openalex.org/W2798766386","https://openalex.org/W2799226512","https://openalex.org/W2898801856","https://openalex.org/W2903451074","https://openalex.org/W2950201748","https://openalex.org/W2951689921","https://openalex.org/W2962745355","https://openalex.org/W2962791457","https://openalex.org/W2962933129","https://openalex.org/W2963092340","https://openalex.org/W2963317585","https://openalex.org/W2963404710","https://openalex.org/W2963430672","https://openalex.org/W2963481221","https://openalex.org/W2963755523","https://openalex.org/W2963959597","https://openalex.org/W2964156132","https://openalex.org/W2964204240","https://openalex.org/W2964210434","https://openalex.org/W2964225338","https://openalex.org/W2971190113","https://openalex.org/W2995872122","https://openalex.org/W3027190643","https://openalex.org/W3029645440","https://openalex.org/W3039791234","https://openalex.org/W3090169104","https://openalex.org/W3097981256","https://openalex.org/W3103457637","https://openalex.org/W3167970296","https://openalex.org/W4248510537","https://openalex.org/W4250589301","https://openalex.org/W4250739957","https://openalex.org/W4253284464","https://openalex.org/W4289147437","https://openalex.org/W4292230442","https://openalex.org/W4297686031","https://openalex.org/W6686778025","https://openalex.org/W6712153814","https://openalex.org/W6713869322","https://openalex.org/W6719853796","https://openalex.org/W6720643467","https://openalex.org/W6726983090","https://openalex.org/W6727883105","https://openalex.org/W6729214561","https://openalex.org/W6734280532","https://openalex.org/W6735923916","https://openalex.org/W6741259694","https://openalex.org/W6743980561","https://openalex.org/W6747381837","https://openalex.org/W6748278370","https://openalex.org/W6750666316","https://openalex.org/W6752307458","https://openalex.org/W6755725002","https://openalex.org/W6757872972","https://openalex.org/W6764252197","https://openalex.org/W6771964890"],"related_works":["https://openalex.org/W2162899405","https://openalex.org/W3113091479","https://openalex.org/W941090075","https://openalex.org/W2044987316","https://openalex.org/W2237480245","https://openalex.org/W3136579521","https://openalex.org/W2021599769","https://openalex.org/W1523179148","https://openalex.org/W2943700667","https://openalex.org/W1998951362"],"abstract_inverted_index":{"In":[0,117],"this":[1,42],"article,":[2],"we":[3,44,119],"study":[4,155],"the":[5,15,22,34,46,60,88,93,100,110,114,123,127,134,143,150,156,159,175,180],"landscape":[6],"of":[7,36,41,48,62,92,102,113,133,158],"an":[8,72],"online":[9],"nonconvex":[10,67],"optimization":[11,95],"problem,":[12,43,181],"for":[13],"which":[14,182],"input":[16],"data":[17,128,177],"vary":[18],"over":[19,190],"time":[20,145],"and":[21,167],"solution":[23,40,65,152],"is":[24,106,125],"a":[25,29,38,57,79,163],"trajectory":[26,105,166],"rather":[27],"than":[28],"single":[30],"point.":[31],"To":[32],"understand":[33],"complexity":[35],"finding":[37],"global":[39,151],"introduce":[45],"notion":[47,61],"<italic":[49],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[50],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">spurious":[51],"(i.e.,":[52],"nonglobal)":[53],"local":[54,64,90,104,140,164,188],"trajectory</i>":[55],"as":[56],"generalization":[58],"to":[59,109,146,149],"spurious":[63,89,103],"in":[66,179],"(time-invariant)":[68],"optimization.":[69],"We":[70,97,154],"develop":[71],"ordinary":[73],"differential":[74],"equation":[75],"(ODE)":[76],"associated":[77],"with":[78],"time-varying":[80,94],"nonlinear":[81],"dynamical":[82,160],"system":[83,161],"which,":[84],"at":[85,138,142],"limit,":[86],"characterizes":[87],"solutions":[91],"problem.":[96],"prove":[98],"that":[99,121],"absence":[101],"closely":[107],"related":[108],"transient":[111],"behavior":[112],"developed":[115],"system.":[116],"particular,":[118],"show":[120,168],"if":[122],"problem":[124],"time-varying,":[126],"variation":[129,178],"may":[130,183],"force":[131],"all":[132],"ODE":[135],"trajectories":[136],"initialized":[137],"arbitrary":[139],"minima":[141,189],"initial":[144],"gradually":[147],"converge":[148],"trajectory.":[153],"Jacobian":[157],"along":[162],"minimum":[165],"how":[169],"its":[170],"eigenvalues":[171],"are":[172],"manipulated":[173],"by":[174],"natural":[176],"consequently":[184],"trigger":[185],"escaping":[186],"poor":[187],"time.":[191]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
