{"id":"https://openalex.org/W4389640200","doi":"https://doi.org/10.1080/00207160.2023.2294688","title":"Adaptation and assessement of projected Nesterov accelerated gradient flow to compute stationary states of nonlinear Schr\u00f6dinger equations","display_name":"Adaptation and assessement of projected Nesterov accelerated gradient flow to compute stationary states of nonlinear Schr\u00f6dinger equations","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4389640200","doi":"https://doi.org/10.1080/00207160.2023.2294688"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2023.2294688","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/00207160.2023.2294688","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-04270784/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062182120","display_name":"Xavier Antoine","orcid":"https://orcid.org/0000-0002-6501-7757"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Xavier Antoine","raw_affiliation_strings":["CNRS, Inria, IECL, Universit\u00e9 de Lorraine, Vandoeuvre-l\u00e8s-Nancy Cedex, France"],"affiliations":[{"raw_affiliation_string":"CNRS, Inria, IECL, Universit\u00e9 de Lorraine, Vandoeuvre-l\u00e8s-Nancy Cedex, France","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5093477238","display_name":"Chorouq Bentayaa","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Chorouq Bentayaa","raw_affiliation_strings":["CNRS, Inria, IECL, Universit\u00e9 de Lorraine, Vandoeuvre-l\u00e8s-Nancy Cedex, France"],"affiliations":[{"raw_affiliation_string":"CNRS, Inria, IECL, Universit\u00e9 de Lorraine, Vandoeuvre-l\u00e8s-Nancy Cedex, France","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089941465","display_name":"J\u00e9r\u00e9mie Gaidamour","orcid":"https://orcid.org/0000-0001-9042-0495"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00e9mie Gaidamour","raw_affiliation_strings":["CNRS, Inria, IECL, Universit\u00e9 de Lorraine, Vandoeuvre-l\u00e8s-Nancy Cedex, France"],"affiliations":[{"raw_affiliation_string":"CNRS, Inria, IECL, Universit\u00e9 de Lorraine, Vandoeuvre-l\u00e8s-Nancy Cedex, France","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062182120"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I3017839442","https://openalex.org/I90183372"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28382098,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"101","issue":"1","first_page":"21","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.6714133024215698},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.615803599357605},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5699580907821655},{"id":"https://openalex.org/keywords/proximal-gradient-methods","display_name":"Proximal Gradient Methods","score":0.5691315531730652},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5494567155838013},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5197439193725586},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4777745008468628},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.476802796125412},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43814417719841003},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4116228520870209},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3637378513813019},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22495737671852112},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10367262363433838},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10226398706436157}],"concepts":[{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.6714133024215698},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.615803599357605},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5699580907821655},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.5691315531730652},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5494567155838013},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5197439193725586},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4777745008468628},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.476802796125412},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43814417719841003},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4116228520870209},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3637378513813019},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22495737671852112},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10367262363433838},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10226398706436157},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207160.2023.2294688","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1080/00207160.2023.2294688","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-04270784v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04270784","pdf_url":"https://hal.science/hal-04270784/document","source":{"id":"https://openalex.org/S4406922454","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.science/hal-04270784","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-04270784v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04270784","pdf_url":"https://hal.science/hal-04270784/document","source":{"id":"https://openalex.org/S4406922454","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.science/hal-04270784","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320310925","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4389640200.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W1494364037","https://openalex.org/W1983530220","https://openalex.org/W1989233441","https://openalex.org/W1992126849","https://openalex.org/W2050338742","https://openalex.org/W2064726339","https://openalex.org/W2071438440","https://openalex.org/W2085565258","https://openalex.org/W2102945680","https://openalex.org/W2108533466","https://openalex.org/W2116323997","https://openalex.org/W2122716160","https://openalex.org/W2124541940","https://openalex.org/W2127447444","https://openalex.org/W2147014517","https://openalex.org/W2228017982","https://openalex.org/W2277337617","https://openalex.org/W2293346537","https://openalex.org/W2528062157","https://openalex.org/W2550808303","https://openalex.org/W2609070549","https://openalex.org/W2755554325","https://openalex.org/W2790724874","https://openalex.org/W2804346888","https://openalex.org/W2922898532","https://openalex.org/W2951248065","https://openalex.org/W2964131920","https://openalex.org/W3101835573","https://openalex.org/W3103611906","https://openalex.org/W3105240523","https://openalex.org/W3127420056"],"related_works":["https://openalex.org/W2916278477","https://openalex.org/W3153752017","https://openalex.org/W2804400349","https://openalex.org/W4297153560","https://openalex.org/W4387635768","https://openalex.org/W2964186284","https://openalex.org/W2058485202","https://openalex.org/W4246345140","https://openalex.org/W3208916810","https://openalex.org/W2985979428"],"abstract_inverted_index":{"The":[0],"aim":[1],"of":[2,37,55,80,125,138,157],"the":[3,12,77,103,114,123,126,136,139,143,155,158],"paper":[4],"is":[5,94],"to":[6,75,122,134,145,163],"derive":[7],"minimization":[8],"algorithms":[9,140],"based":[10],"on":[11,64],"Nesterov":[13,104,159],"accelerated":[14,105,160],"gradient":[15,98,106,161],"flow":[16,99,107,162],"[Y.":[17],"Nesterov,":[18,34,61],"Gradient":[19],"methods":[20],"for":[21],"minimizing":[22],"composite":[23],"objective":[24],"function.":[25],"Core":[26],"discussion":[27],"paper,":[28],"(2007).":[29],"Available":[30],"at":[31,113],"http://www.ecore.be/DPs/dp_1191313936.pdf;":[32],"Y.":[33,60],"A":[35,67,92,128],"method":[36],"solving":[38],"a":[39,88],"convex":[40],"programming":[41],"problem":[42],"with":[43,96],"convergence":[44],"rate":[45],"O(1/k2).":[46],"In":[47],"Doklady":[48],"Akademii":[49],"Nauk,":[50],"Vol.":[51],"269,":[52],"Russian":[53],"Academy":[54],"Sciences,":[56],"1983,":[57],"pp.":[58],"543\u2013547;":[59],"Introductory":[62],"Lectures":[63],"Convex":[65],"Optimization:":[66],"basic":[68],"course,":[69],"Kluwer":[70],"Academic":[71],"Publishers,":[72],"Massachusetts,":[73],"2004.]":[74],"compute":[76],"ground":[78],"state":[79],"nonlinear":[81,164],"Schr\u00f6dinger":[82,165],"equations,":[83],"which":[84],"can":[85],"potentially":[86],"include":[87],"fractional":[89],"laplacian":[90],"term.":[91],"comparison":[93],"developed":[95],"standard":[97],"formulations":[100],"showing":[101],"that":[102,149],"has":[108],"some":[109,119],"interesting":[110],"properties":[111],"but":[112],"same":[115],"time":[116],"finds":[117],"also":[118],"limitations":[120],"due":[121],"nature":[124],"problem.":[127],"few":[129],"simulations":[130],"are":[131],"finally":[132],"reported":[133],"understand":[135],"behaviour":[137],"and":[141],"open":[142],"path":[144],"further":[146],"complicate":[147],"questions":[148],"require":[150],"more":[151],"advanced":[152],"studies":[153],"concerning":[154],"application":[156],"equations.":[166]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
