{"id":"https://openalex.org/W1979207064","doi":"https://doi.org/10.1137/s0363012902410861","title":"Barrier Operators and Associated Gradient-Like Dynamical Systems for Constrained Minimization Problems","display_name":"Barrier Operators and Associated Gradient-Like Dynamical Systems for Constrained Minimization Problems","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W1979207064","doi":"https://doi.org/10.1137/s0363012902410861","mag":"1979207064"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012902410861","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012902410861","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5049386571","display_name":"J\u00e9r\u00f4me Bolte","orcid":"https://orcid.org/0000-0002-1676-8407"},"institutions":[{"id":"https://openalex.org/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00f4me Bolte","raw_affiliation_strings":["Montpellier 2 University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Montpellier 2 University","institution_ids":["https://openalex.org/I19894307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041397571","display_name":"Marc Teboulle","orcid":"https://orcid.org/0000-0002-4228-131X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Marc Teboulle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.184,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.87034961,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"42","issue":"4","first_page":"1266","last_page":"1292"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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":0.9987999796867371,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.940500020980835,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7769858837127686},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6552431583404541},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.5996875166893005},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.5568211078643799},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5350452661514282},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4675558805465698},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.46547505259513855},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.45503732562065125},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.4546518623828888},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4501478672027588},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4357355237007141},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.4284767508506775},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4100545346736908},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3802753984928131},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15733817219734192},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.093360036611557}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7769858837127686},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6552431583404541},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5996875166893005},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.5568211078643799},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5350452661514282},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4675558805465698},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.46547505259513855},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.45503732562065125},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.4546518623828888},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4501478672027588},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4357355237007141},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.4284767508506775},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4100545346736908},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3802753984928131},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15733817219734192},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.093360036611557},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0363012902410861","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012902410861","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:publications.ut-capitole.fr:3437","is_oa":false,"landing_page_url":"http://tse-fr.eu/pub/23278","pdf_url":null,"source":{"id":"https://openalex.org/S4306401603","display_name":"Toulouse Capitole Publications (University Toulouse 1 Capitole)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I3131550300","host_organization_name":"Universit\u00e9 Toulouse-I-Capitole","host_organization_lineage":["https://openalex.org/I3131550300"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W199410564","https://openalex.org/W257442556","https://openalex.org/W1238699803","https://openalex.org/W1582617215","https://openalex.org/W1590824230","https://openalex.org/W1632601927","https://openalex.org/W1967960319","https://openalex.org/W1968699683","https://openalex.org/W1984958640","https://openalex.org/W1997427529","https://openalex.org/W2004304255","https://openalex.org/W2009274429","https://openalex.org/W2011243226","https://openalex.org/W2013243898","https://openalex.org/W2021472025","https://openalex.org/W2029465407","https://openalex.org/W2040874526","https://openalex.org/W2052895085","https://openalex.org/W2053487511","https://openalex.org/W2056014954","https://openalex.org/W2063357812","https://openalex.org/W2064404969","https://openalex.org/W2067272684","https://openalex.org/W2070815098","https://openalex.org/W2090376964","https://openalex.org/W2091760073","https://openalex.org/W2112980792","https://openalex.org/W2118369604","https://openalex.org/W2123825652","https://openalex.org/W2132488568","https://openalex.org/W2315925303","https://openalex.org/W2587712072","https://openalex.org/W4210718478","https://openalex.org/W4238957126","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W2811217697","https://openalex.org/W4385644471","https://openalex.org/W4320495396","https://openalex.org/W2564172750","https://openalex.org/W2041341337","https://openalex.org/W2037966176","https://openalex.org/W2026452100","https://openalex.org/W2372778757","https://openalex.org/W2112655684","https://openalex.org/W2067693696"],"abstract_inverted_index":{"We":[0,122],"study":[1],"some":[2,117],"continuous":[3,51,64,74],"dynamical":[4,36,163],"systems":[5,164],"associated":[6,32],"with":[7,215],"constrained":[8],"optimization":[9],"problems.":[10],"For":[11],"that":[12],"purpose,":[13],"we":[14,147,168],"introduce":[15],"the":[16,31,57,131,142,149,155,159,174,178,209],"concept":[17],"of":[18,34,130,134,154,162,177,180,185],"elliptic":[19,205],"barrier":[20,206],"operators":[21],"and":[22,29,68,83,101,113,119,126],"develop":[23],"a":[24,137,170,183,186,190],"unified":[25],"framework":[26,112],"to":[27,46,182,199],"derive":[28,169],"analyze":[30,148],"class":[33,48,161],"gradient-like":[35],"systems,":[37],"called":[38],"A-driven":[39],"descent":[40,52,62,76],"method":[41],"(A-DM).":[42,165],"Prominent":[43],"methods":[44,53,67,70,77,90],"belonging":[45],"this":[47],"include":[49],"several":[50,200],"studied":[54],"earlier":[55],"in":[56],"literature":[58],"such":[59,78,91],"as":[60,71,73,79,92],"steepest":[61],"method,":[63],"gradient":[65,85],"projection":[66],"Newton-type":[69],"well":[72],"interior":[75,94],"Lotka-Volterra-type":[80],"differential":[81],"equations":[82],"Riemannian":[84],"methods.":[86],"Related":[87],"discrete":[88],"iterative":[89],"proximal":[93],"point":[95],"algorithms":[96],"based":[97],"on":[98],"Bregman":[99],"functions":[100],"second":[102],"order":[103],"homogeneous":[104],"kernels":[105],"can":[106],"also":[107],"be":[108],"recovered":[109],"within":[110],"our":[111,211],"allow":[114],"for":[115,136],"deriving":[116],"new":[118],"interesting":[120],"dynamics.":[121],"prove":[123],"global":[124,175],"existence":[125],"strong":[127],"viability":[128],"results":[129,212],"corresponding":[132],"trajectories":[133],"(A-DM)":[135,181],"smooth":[138],"objective":[139,143],"function.":[140],"When":[141],"function":[144,188],"is":[145,196],"convex,":[146],"asymptotic":[150],"behavior":[151],"at":[152],"infinity":[153],"trajectory":[156,179],"produced":[157],"by":[158],"proposed":[160],"In":[166],"particular,":[167],"general":[171],"criterion":[172],"ensuring":[173],"convergence":[176],"minimizer":[184],"convex":[187,192],"over":[189],"closed":[191],"set.":[193],"This":[194],"result":[195],"then":[197],"applied":[198],"dynamics":[201],"built":[202],"upon":[203],"specific":[204],"operators.":[207],"Throughout":[208],"paper,":[210],"are":[213],"illustrated":[214],"many":[216],"examples.":[217]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
