{"id":"https://openalex.org/W2055954415","doi":"https://doi.org/10.1137/s0363012902419977","title":"Hessian Riemannian Gradient Flows in Convex Programming","display_name":"Hessian Riemannian Gradient Flows in Convex Programming","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2055954415","doi":"https://doi.org/10.1137/s0363012902419977","mag":"2055954415"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012902419977","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012902419977","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10533/175566","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Felipe Alvarez","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Felipe Alvarez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"J\u00e9r\u00f4me Bolte","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00f4me Bolte","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Olivier Brahic","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olivier Brahic","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3845,"has_fulltext":false,"cited_by_count":69,"citation_normalized_percentile":{"value":0.81073507,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"43","issue":"2","first_page":"477","last_page":"501"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.7962999939918518,"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":0.7962999939918518,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.05950000137090683,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.03799999877810478,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7573000192642212},{"id":"https://openalex.org/keywords/hessian-equation","display_name":"Hessian equation","score":0.5115000009536743},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.49779999256134033},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.45489999651908875},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.44029998779296875},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.42320001125335693},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4077000021934509},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.3776000142097473},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.3714999854564667}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8604999780654907},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7573000192642212},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5123000144958496},{"id":"https://openalex.org/C73729460","wikidata":"https://www.wikidata.org/wiki/Q17023339","display_name":"Hessian equation","level":4,"score":0.5115000009536743},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.49779999256134033},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.45489999651908875},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.44029998779296875},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4318000078201294},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.42320001125335693},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4077000021934509},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3776000142097473},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.3714999854564667},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.36079999804496765},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3343000113964081},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3174999952316284},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.31450000405311584},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.2973000109195709},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.28369998931884766},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.2587999999523163},{"id":"https://openalex.org/C523394659","wikidata":"https://www.wikidata.org/wiki/Q17086892","display_name":"Variational analysis","level":2,"score":0.25839999318122864},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.25619998574256897}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/s0363012902419977","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012902419977","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:localhost:10533/175566","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/175566","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM JOURNAL ON CONTROL AND OPTIMIZATION (PRINT)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:1811.10331","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1811.10331","pdf_url":"https://arxiv.org/pdf/1811.10331","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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:HAL:hal-01928141v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01928141","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"SIAM Journal on Control and Optimization, 2004, 43 (2), pp.477 - 501. &#x27E8;10.1137/S0363012902419977&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:americanae.aecid.es:3268606","is_oa":true,"landing_page_url":"http://americanae.aecid.es/americanae/es/registros/registro.do?tipoRegistro=MTD&idBib=3268606","pdf_url":null,"source":{"id":"https://openalex.org/S4306400786","display_name":"Americanae (AECID Library)","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":"SIAM JOURNAL ON CONTROL AND OPTIMIZATION (PRINT)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:repositorio.uchile.cl:2250/125794","is_oa":false,"landing_page_url":"http://repositorio.uchile.cl/handle/2250/125794","pdf_url":null,"source":{"id":"https://openalex.org/S4306481413","display_name":"Universidad de Chile","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Art\u00edculo de revista"}],"best_oa_location":{"id":"pmh:oai:localhost:10533/175566","is_oa":true,"landing_page_url":"http://hdl.handle.net/10533/175566","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM JOURNAL ON CONTROL AND OPTIMIZATION (PRINT)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W1968699683","https://openalex.org/W1979207064","https://openalex.org/W1982143037","https://openalex.org/W1984958640","https://openalex.org/W1997427529","https://openalex.org/W2004304255","https://openalex.org/W2009274429","https://openalex.org/W2011243226","https://openalex.org/W2021472025","https://openalex.org/W2033231393","https://openalex.org/W2038151469","https://openalex.org/W2064404969","https://openalex.org/W2067272684","https://openalex.org/W2084324591","https://openalex.org/W2085728653","https://openalex.org/W2089725613","https://openalex.org/W2089876425","https://openalex.org/W2090376964","https://openalex.org/W2090806510","https://openalex.org/W2091760073","https://openalex.org/W2111965642","https://openalex.org/W2113416387","https://openalex.org/W2123825652","https://openalex.org/W2133776435","https://openalex.org/W2137252934","https://openalex.org/W2154059477","https://openalex.org/W2611147814","https://openalex.org/W2920822263","https://openalex.org/W4206033904","https://openalex.org/W4210605524","https://openalex.org/W4246883249","https://openalex.org/W4249513058","https://openalex.org/W4249667877"],"related_works":[],"abstract_inverted_index":{"In":[0,119],"view":[1],"of":[2,12,56,80,86,122,130,137,142,153,156],"solving":[3],"theoretically":[4],"constrained":[5],"minimization":[6],"problems,":[7],"we":[8],"investigate":[9],"the":[10,13,54,60,78,120,131],"properties":[11],"gradient":[14,88],"flows":[15,89],"with":[16,44,74,108],"respect":[17,45],"to":[18,46],"Hessian":[19,30],"Riemannian":[20,31],"metrics":[21,37],"induced":[22],"by":[23],"Legendre":[24],"functions.":[25],"The":[26],"first":[27],"result":[28],"characterizes":[29],"structures":[32],"on":[33],"convex":[34,81,106],"sets":[35],"as":[36],"that":[38],"have":[39],"a":[40,50,105,123],"specific":[41],"integration":[42],"property":[43],"variational":[47],"inequalities,":[48],"giving":[49],"new":[51],"motivation":[52],"for":[53,99,104,147],"introduction":[55],"Bregman-type":[57,143],"distances.":[58],"Then,":[59],"general":[61],"evolution":[62],"problem":[63],"is":[64,69],"introduced,":[65],"and":[66,96,110,151,160],"global":[67],"convergence":[68,101,114],"established":[70],"under":[71],"quasi-convexity":[72],"conditions,":[73],"interesting":[75],"refinements":[76],"in":[77],"case":[79,121],"minimization.":[82],"Some":[83,113],"explicit":[84],"examples":[85],"these":[87],"are":[90,94,102,117,133],"discussed.":[91],"Dual":[92],"trajectories":[93],"identified,":[95],"sufficient":[97],"conditions":[98],"dual":[100],"examined":[103],"program":[107],"positivity":[109],"equality":[111],"constraints.":[112],"rate":[115],"results":[116],"established.":[118],"linear":[124],"objective":[125],"function,":[126],"several":[127],"optimality":[128],"characterizations":[129],"orbits":[132],"given:":[134],"optimal":[135],"path":[136],"viscosity":[138],"methods,":[139],"continuous-time":[140],"model":[141],"proximal":[144],"algorithms,":[145],"geodesics":[146],"some":[148,157],"adequate":[149],"metrics,":[150],"projections":[152],"$\\dot":[154],"q$-trajectories":[155],"Lagrange":[158],"equations":[159],"completely":[161],"integrable":[162],"Hamiltonian":[163],"systems.":[164]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}
