{"id":"https://openalex.org/W2768923100","doi":"https://doi.org/10.1137/19m1304210","title":"Accelerated Optimization in the PDE Framework Formulations for the Active Contour Case","display_name":"Accelerated Optimization in the PDE Framework Formulations for the Active Contour Case","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2768923100","doi":"https://doi.org/10.1137/19m1304210","mag":"2768923100","pmid":"https://pubmed.ncbi.nlm.nih.gov/34336084"},"language":"en","primary_location":{"id":"doi:10.1137/19m1304210","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1304210","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Journal on Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1711.09867","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014124403","display_name":"Anthony Yezzi","orcid":"https://orcid.org/0000-0002-3771-4889"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anthony Yezzi","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Georgia Institute of Technology 30332 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Georgia Institute of Technology 30332 USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012065009","display_name":"Ganesh Sundaramoorthi","orcid":"https://orcid.org/0000-0003-3471-6384"},"institutions":[{"id":"https://openalex.org/I4210091334","display_name":"Raytheon Technologies (Italy)","ror":"https://ror.org/00fg6nx42","country_code":"IT","type":"company","lineage":["https://openalex.org/I1306686416","https://openalex.org/I4210091334"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Ganesh Sundaramoorthi","raw_affiliation_strings":["Raytheon Technologies Research Center"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Raytheon Technologies Research Center","institution_ids":["https://openalex.org/I4210091334"]}]},{"author_position":"last","author":{"id":null,"display_name":"Minas Benyamin","orcid":"https://orcid.org/0000-0001-9303-635X"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Minas Benyamin","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Georgia Institute of Technology 30332 USA"],"raw_orcid":"https://orcid.org/0000-0001-9303-635X","affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Georgia Institute of Technology 30332 USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2684,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.64094379,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"13","issue":"4","first_page":"2029","last_page":"2062"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9991000294685364,"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/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.9991000294685364,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9984999895095825,"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/gradient-descent","display_name":"Gradient descent","score":0.6693745255470276},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5897617936134338},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5295644402503967},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5284982323646545},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.5108827948570251},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.5060808062553406},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.476481169462204},{"id":"https://openalex.org/keywords/bayesian-optimization","display_name":"Bayesian optimization","score":0.4202902913093567},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35268545150756836},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14778825640678406},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.1260921061038971}],"concepts":[{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6693745255470276},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5897617936134338},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5295644402503967},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5284982323646545},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.5108827948570251},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.5060808062553406},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.476481169462204},{"id":"https://openalex.org/C2778049539","wikidata":"https://www.wikidata.org/wiki/Q17002908","display_name":"Bayesian optimization","level":2,"score":0.4202902913093567},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35268545150756836},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14778825640678406},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.1260921061038971},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/19m1304210","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1304210","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Journal on Imaging Sciences","raw_type":"journal-article"},{"id":"pmid:34336084","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34336084","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM journal on imaging sciences","raw_type":null},{"id":"pmh:oai:arXiv.org:1711.09867","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1711.09867","pdf_url":"https://arxiv.org/pdf/1711.09867","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/626461","is_oa":true,"landing_page_url":"http://hdl.handle.net/10754/626461","pdf_url":"http://hdl.handle.net/10754/626461","source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Preprint"},{"id":"mag:2768923100","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1711.09867.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:8320808","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8320808","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM J Imaging Sci","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1711.09867","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1711.09867","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1711.09867","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1711.09867","pdf_url":"https://arxiv.org/pdf/1711.09867","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4104320779","display_name":null,"funder_award_id":"R01 HL143350","funder_id":"https://openalex.org/F4320337338","funder_display_name":"National Heart, Lung, and Blood Institute"},{"id":"https://openalex.org/G501257308","display_name":null,"funder_award_id":"R01-HL-143350","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G7871023607","display_name":null,"funder_award_id":"W911NF-18-1-0281","funder_id":"https://openalex.org/F4320338295","funder_display_name":"Army Research Laboratory"}],"funders":[{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320337338","display_name":"National Heart, Lung, and Blood Institute","ror":"https://ror.org/012pb6c26"},{"id":"https://openalex.org/F4320338295","display_name":"Army Research Laboratory","ror":"https://ror.org/011hc8f90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":49,"referenced_works":["https://openalex.org/W1238092070","https://openalex.org/W1578285471","https://openalex.org/W1582924027","https://openalex.org/W1585160083","https://openalex.org/W1604679511","https://openalex.org/W1946256299","https://openalex.org/W1977109023","https://openalex.org/W1985506636","https://openalex.org/W1987083649","https://openalex.org/W1987579928","https://openalex.org/W1991113069","https://openalex.org/W1998635907","https://openalex.org/W2008429370","https://openalex.org/W2009941369","https://openalex.org/W2030161963","https://openalex.org/W2038495454","https://openalex.org/W2055686029","https://openalex.org/W2055834603","https://openalex.org/W2058190079","https://openalex.org/W2067193435","https://openalex.org/W2090903445","https://openalex.org/W2092663520","https://openalex.org/W2104358837","https://openalex.org/W2105492237","https://openalex.org/W2106518569","https://openalex.org/W2113038546","https://openalex.org/W2116040950","https://openalex.org/W2127447444","https://openalex.org/W2128962323","https://openalex.org/W2130883754","https://openalex.org/W2135095945","https://openalex.org/W2138086725","https://openalex.org/W2140274166","https://openalex.org/W2153749284","https://openalex.org/W2155697938","https://openalex.org/W2167302917","https://openalex.org/W2167732364","https://openalex.org/W2184596805","https://openalex.org/W2184634347","https://openalex.org/W2528062157","https://openalex.org/W2607390531","https://openalex.org/W2765393161","https://openalex.org/W2913225681","https://openalex.org/W2963430672","https://openalex.org/W2963480765","https://openalex.org/W2977571291","https://openalex.org/W3038698521","https://openalex.org/W3141595720","https://openalex.org/W3211330693"],"related_works":["https://openalex.org/W2963430672","https://openalex.org/W2948412125","https://openalex.org/W2891625925","https://openalex.org/W2795434836","https://openalex.org/W2116040950","https://openalex.org/W1988720110","https://openalex.org/W104184427","https://openalex.org/W3169535361","https://openalex.org/W2202258464","https://openalex.org/W3014549192","https://openalex.org/W2804589149","https://openalex.org/W2954645219","https://openalex.org/W3012021832","https://openalex.org/W2912961847","https://openalex.org/W2784019040","https://openalex.org/W155824844","https://openalex.org/W2951958592","https://openalex.org/W2953881522","https://openalex.org/W2894831786","https://openalex.org/W3211659246"],"abstract_inverted_index":{"Following":[0],"the":[1,15,57,88,104,143,167,176,183,198,203,215,219,226],"seminal":[2],"work":[3],"of":[4,17,56,82,131,170,200,217,229,239],"Nesterov,":[5],"accelerated":[6,37,95,132,230],"optimization":[7,27,204,220,233],"methods":[8,100],"have":[9],"been":[10],"used":[11],"to":[12,86,147,160,235],"powerfully":[13],"boost":[14],"performance":[16],"first-order,":[18],"gradient":[19,38,45,98],"based":[20,232],"parameter":[21,58],"estimation":[22],"in":[23,120,137,195],"scenarios":[24],"where":[25],"second-order":[26],"strategies":[28],"are":[29],"either":[30],"inapplicable":[31],"or":[32],"impractical.":[33],"Not":[34],"only":[35,76],"does":[36],"descent":[39],"converge":[40],"considerably":[41],"faster":[42],"than":[43],"traditional":[44],"descent,":[46],"but":[47],"it":[48,68],"also":[49,224],"performs":[50],"a":[51,71,80,128,138,189],"more":[52],"robust":[53],"local":[54,77],"search":[55,99],"space":[59,169,185],"by":[60,174],"initially":[61],"overshooting":[62],"and":[63,96,124,172,186],"then":[64],"oscillating":[65],"back":[66],"as":[67],"settles":[69],"into":[70],"final":[72],"configuration,":[73],"thereby":[74],"selecting":[75],"minimizers":[78],"with":[79,166,179,197,221],"basis":[81],"attraction":[83],"large":[84],"enough":[85],"contain":[87],"initial":[89],"overshoot.":[90],"This":[91],"behavior":[92],"has":[93],"made":[94],"stochastic":[97],"particularly":[101],"popular":[102],"within":[103],"machine":[105],"learning":[106],"community.":[107],"In":[108],"their":[109,154],"recent":[110],"PNAS":[111],"2016":[112],"paper,":[113],"A":[114],"Variational":[115],"Perspective":[116],"on":[117,182],"Accelerated":[118],"Methods":[119],"Optimization,":[121],"Wibisono,":[122],"Wilson,":[123],"Jordan":[125],"demonstrate":[126],"how":[127,153],"broad":[129],"class":[130,228],"schemes":[133,234],"can":[134],"be":[135,157],"cast":[136],"variational":[139],"framework":[140],"formulated":[141],"around":[142],"Bregman":[144,177],"divergence,":[145],"leading":[146],"continuum":[148],"limit":[149],"ODEs.":[150],"We":[151],"show":[152],"formulation":[155],"may":[156],"further":[158],"extended":[159],"infinite":[161],"dimensional":[162],"manifolds":[163],"(starting":[164],"here":[165],"geometric":[168],"curves":[171],"surfaces)":[173],"substituting":[175],"divergence":[178],"inner":[180],"products":[181],"tangent":[184],"explicitly":[187],"introducing":[188],"distributed":[190],"mass":[191,208,241],"model":[192],"which":[193,210],"evolves":[194],"conjunction":[196],"object":[199],"interest":[201],"during":[202],"process.":[205],"The":[206],"coevolving":[207],"model,":[209],"is":[211],"introduced":[212],"purely":[213],"for":[214],"sake":[216],"endowing":[218],"helpful":[222],"dynamics,":[223],"links":[225],"resulting":[227],"PDE":[231],"fluid":[236],"dynamical":[237],"formulations":[238],"optimal":[240],"transport.":[242]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}