{"id":"https://openalex.org/W3118436368","doi":"https://doi.org/10.1109/cdc42340.2020.9304412","title":"On the transient growth of Nesterov\u2019s accelerated method for strongly convex optimization problems","display_name":"On the transient growth of Nesterov\u2019s accelerated method for strongly convex optimization problems","publication_year":2020,"publication_date":"2020-12-14","ids":{"openalex":"https://openalex.org/W3118436368","doi":"https://doi.org/10.1109/cdc42340.2020.9304412","mag":"3118436368"},"language":"en","primary_location":{"id":"doi:10.1109/cdc42340.2020.9304412","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc42340.2020.9304412","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 59th IEEE Conference on Decision and Control (CDC)","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/A5012567706","display_name":"Samantha Samuelson","orcid":"https://orcid.org/0000-0003-4797-6302"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Samantha Samuelson","raw_affiliation_strings":["University of Southern California, Los Angeles, CA"],"affiliations":[{"raw_affiliation_string":"University of Southern California, Los Angeles, CA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047399398","display_name":"Hesameddin Mohammadi","orcid":"https://orcid.org/0000-0003-3030-1536"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hesameddin Mohammadi","raw_affiliation_strings":["University of Southern California, Los Angeles, CA"],"affiliations":[{"raw_affiliation_string":"University of Southern California, Los Angeles, CA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087790067","display_name":"Mihailo R. Jovanovi\u0107","orcid":"https://orcid.org/0000-0002-4181-2924"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mihailo R. Jovanovic","raw_affiliation_strings":["University of Southern California, Los Angeles, CA"],"affiliations":[{"raw_affiliation_string":"University of Southern California, Los Angeles, CA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012567706"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":0.1761,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49001233,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"87","issue":null,"first_page":"5911","last_page":"5916"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9995999932289124,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9986000061035156,"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/mathematics","display_name":"Mathematics","score":0.6304860711097717},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5906890630722046},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5660574436187744},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.5439685583114624},{"id":"https://openalex.org/keywords/transient","display_name":"Transient (computer programming)","score":0.5417649149894714},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5348148941993713},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5318040251731873},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5300079584121704},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5055069923400879},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49715521931648254},{"id":"https://openalex.org/keywords/euclidean-distance","display_name":"Euclidean distance","score":0.48982927203178406},{"id":"https://openalex.org/keywords/square-root","display_name":"Square root","score":0.4666447937488556},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4638875126838684},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.45187777280807495},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.44685935974121094},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2918434143066406},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20292097330093384}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6304860711097717},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5906890630722046},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5660574436187744},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.5439685583114624},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.5417649149894714},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5348148941993713},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5318040251731873},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5300079584121704},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5055069923400879},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49715521931648254},{"id":"https://openalex.org/C120174047","wikidata":"https://www.wikidata.org/wiki/Q847073","display_name":"Euclidean distance","level":2,"score":0.48982927203178406},{"id":"https://openalex.org/C11577676","wikidata":"https://www.wikidata.org/wiki/Q134237","display_name":"Square root","level":2,"score":0.4666447937488556},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4638875126838684},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.45187777280807495},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.44685935974121094},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2918434143066406},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20292097330093384},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc42340.2020.9304412","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc42340.2020.9304412","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 59th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W104184427","https://openalex.org/W1409984952","https://openalex.org/W1988720110","https://openalex.org/W2030161963","https://openalex.org/W2097460613","https://openalex.org/W2097944741","https://openalex.org/W2100556411","https://openalex.org/W2101159990","https://openalex.org/W2124541940","https://openalex.org/W2124768887","https://openalex.org/W2146482778","https://openalex.org/W2210084516","https://openalex.org/W2496350169","https://openalex.org/W2532703171","https://openalex.org/W2536673720","https://openalex.org/W2765203333","https://openalex.org/W2901838001","https://openalex.org/W2913357890","https://openalex.org/W2914211548","https://openalex.org/W2936995161","https://openalex.org/W2962844775","https://openalex.org/W2963007855","https://openalex.org/W2963040514","https://openalex.org/W2963433607","https://openalex.org/W2963811077","https://openalex.org/W2964102336","https://openalex.org/W2971816657","https://openalex.org/W2972329375","https://openalex.org/W3011830603","https://openalex.org/W3042135496","https://openalex.org/W3045725788","https://openalex.org/W3104429825","https://openalex.org/W3106429777","https://openalex.org/W3141595720","https://openalex.org/W4288361651","https://openalex.org/W6604254268","https://openalex.org/W6758704138","https://openalex.org/W6761030284","https://openalex.org/W6762070236","https://openalex.org/W6762499778","https://openalex.org/W6767256672"],"related_works":["https://openalex.org/W2090152127","https://openalex.org/W1965169884","https://openalex.org/W3125580510","https://openalex.org/W2008939113","https://openalex.org/W14679004","https://openalex.org/W1566651525","https://openalex.org/W2977652649","https://openalex.org/W2318206461","https://openalex.org/W37157938","https://openalex.org/W4298154183"],"abstract_inverted_index":{"Compared":[0],"to":[1,53,85,106],"standard":[2],"descent-based":[3],"algorithms,":[4],"accelerated":[5,60],"first-order":[6],"methods":[7],"for":[8],"strongly":[9],"convex":[10],"smooth":[11],"optimization":[12,77],"problems":[13,94],"may":[14],"exhibit":[15],"large":[16,96],"transient":[17,56],"responses.":[18],"For":[19,93],"quadratic":[20,51],"problems,":[21],"this":[22,43,103],"phenomenon":[23],"arises":[24],"from":[25],"the":[26,32,47,55,68,72,76,80,86,90,111],"presence":[27],"of":[28,49,58,71,89,102,113],"non-normal":[29],"dynamics":[30],"and":[31,79],"modes":[33],"that":[34,64],"yield":[35],"an":[36],"algebraic":[37],"growth":[38],"in":[39],"early":[40],"iterations.":[41],"In":[42],"paper,":[44],"we":[45,99],"employ":[46],"framework":[48],"integral":[50],"constraints":[52],"examine":[54],"response":[57],"Nesterov's":[59],"method.":[61],"We":[62],"prove":[63],"a":[65],"bound":[66,104],"on":[67],"largest":[69],"value":[70],"Euclidean":[73],"distance":[74],"between":[75],"variable":[78],"global":[81],"minimizer":[82],"is":[83],"proportional":[84],"square":[87],"root":[88],"condition":[91,97],"number.":[92],"with":[95],"numbers":[98],"demonstrate":[100],"tightness":[101],"up":[105],"constant":[107],"factors,":[108],"thereby":[109],"establishing":[110],"merits":[112],"our":[114],"approach.":[115]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}