{"id":"https://openalex.org/W2077612096","doi":"https://doi.org/10.1137/040605266","title":"Convergence of the Iterates of Descent Methods for Analytic Cost Functions","display_name":"Convergence of the Iterates of Descent Methods for Analytic Cost Functions","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2077612096","doi":"https://doi.org/10.1137/040605266","mag":"2077612096"},"language":"en","primary_location":{"id":"doi:10.1137/040605266","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040605266","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 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/A5075495386","display_name":"Pierre-Antoine Absil","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"P. A. Absil","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011097720","display_name":"Robert Mahony","orcid":"https://orcid.org/0000-0002-7803-2868"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"R. Mahony","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029673479","display_name":"Ben Andrews","orcid":"https://orcid.org/0000-0002-6507-0347"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"B. Andrews","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5075495386"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.7609,"has_fulltext":false,"cited_by_count":300,"citation_normalized_percentile":{"value":0.98098859,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"16","issue":"2","first_page":"531","last_page":"547"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9951000213623047,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9872999787330627,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.849714994430542},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7635326981544495},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.7315495610237122},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6863240599632263},{"id":"https://openalex.org/keywords/limit-point","display_name":"Limit point","score":0.539297878742218},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.531290590763092},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5288689732551575},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5062050223350525},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49117323756217957},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.46824610233306885},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4409814774990082},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4388969838619232},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.4353610873222351},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.42125582695007324},{"id":"https://openalex.org/keywords/analytic-function","display_name":"Analytic function","score":0.4196837246417999},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2535385191440582},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0676526427268982},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.058540016412734985}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.849714994430542},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7635326981544495},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.7315495610237122},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6863240599632263},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.539297878742218},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.531290590763092},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5288689732551575},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5062050223350525},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49117323756217957},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.46824610233306885},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4409814774990082},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4388969838619232},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.4353610873222351},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.42125582695007324},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.4196837246417999},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2535385191440582},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0676526427268982},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.058540016412734985},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040605266","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040605266","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"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 Optimization","raw_type":"journal-article"},{"id":"pmh:oai:dial.uclouvain.be:boreal:38704","is_oa":false,"landing_page_url":"http://hdl.handle.net/2078.1/38704","pdf_url":null,"source":{"id":"https://openalex.org/S4306401974","display_name":"DIAL (Catholic University of Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization, Vol. 16, no. 2, p. 531-547 (2005)","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:openresearch-repository.anu.edu.au:1885/79167","is_oa":false,"landing_page_url":"http://hdl.handle.net/1885/79167","pdf_url":null,"source":{"id":"https://openalex.org/S4306402539","display_name":"ANU Open Research (Australian National University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I118347636","host_organization_name":"Australian National University","host_organization_lineage":["https://openalex.org/I118347636"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Optimization","raw_type":"Journal article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W48894704","https://openalex.org/W147998453","https://openalex.org/W615276906","https://openalex.org/W1509448450","https://openalex.org/W1579664581","https://openalex.org/W1988849934","https://openalex.org/W1995202706","https://openalex.org/W2000389939","https://openalex.org/W2003536293","https://openalex.org/W2008995486","https://openalex.org/W2021484063","https://openalex.org/W2022541060","https://openalex.org/W2044047732","https://openalex.org/W2053334740","https://openalex.org/W2062106836","https://openalex.org/W2064404969","https://openalex.org/W2068484625","https://openalex.org/W2070815098","https://openalex.org/W2075184363","https://openalex.org/W2075194837","https://openalex.org/W2077658674","https://openalex.org/W2080803951","https://openalex.org/W2085563112","https://openalex.org/W2090243370","https://openalex.org/W2105735474","https://openalex.org/W2111885254","https://openalex.org/W2119842211","https://openalex.org/W2153532571","https://openalex.org/W2291661959","https://openalex.org/W2331639718","https://openalex.org/W2567576169","https://openalex.org/W2798766386","https://openalex.org/W3029645440","https://openalex.org/W4210605524","https://openalex.org/W4212997115","https://openalex.org/W4285719527","https://openalex.org/W4293775970","https://openalex.org/W4302598034","https://openalex.org/W4310301864"],"related_works":["https://openalex.org/W4283017538","https://openalex.org/W1996936972","https://openalex.org/W3021699548","https://openalex.org/W2015677538","https://openalex.org/W4291718021","https://openalex.org/W1989888202","https://openalex.org/W1981914421","https://openalex.org/W2377285242","https://openalex.org/W2359783269","https://openalex.org/W197074893"],"abstract_inverted_index":{"In":[0,42],"the":[1,48,111,122,125,132,135],"early":[2],"eighties":[3],"Lojasiewicz":[4],"[in":[5],"Seminari":[6],"di":[7,11,14,17],"Geometria":[8],"1982-1983,":[9],"Universit\u00e0":[10],"Bologna,":[12],"Istituto":[13],"Geometria,":[15],"Dipartimento":[16],"Matematica,":[18],"1984,":[19],"pp.":[20],"115--117]":[21],"proved":[22],"that":[23,47,110],"a":[24,28,38,76,96],"bounded":[25],"solution":[26],"of":[27,50,79,99,102,124,134],"gradient":[29],"flow":[30],"for":[31,54,88,95],"an":[32,55],"analytic":[33,56],"cost":[34,57,100,112,126,136],"function":[35],"converges":[36],"to":[37,75,91],"well-defined":[39],"limit":[40],"point.":[41],"this":[43,60],"paper,":[44],"we":[45],"show":[46],"iterates":[49],"numerical":[51],"descent":[52,68,89],"algorithms,":[53],"function,":[58],"share":[59],"convergence":[61],"property":[62],"if":[63],"they":[64],"satisfy":[65],"certain":[66],"natural":[67],"conditions.":[69],"The":[70,105],"results":[71,87],"obtained":[72],"are":[73],"applicable":[74],"broad":[77],"class":[78,98],"optimization":[80],"schemes":[81],"and":[82,117],"strengthen":[83],"classical":[84],"\"weak":[85],"convergence\"":[86,94],"methods":[90],"\"strong":[92],"limit-point":[93],"large":[97],"functions":[101],"practical":[103],"interest.":[104],"result":[106],"does":[107],"not":[108],"require":[109],"has":[113],"isolated":[114],"critical":[115,138],"points":[116],"requires":[118],"no":[119],"assumptions":[120],"on":[121,131],"convexity":[123],"nor":[127],"any":[128],"nondegeneracy":[129],"conditions":[130],"Hessian":[133],"at":[137],"points.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":16},{"year":2024,"cited_by_count":28},{"year":2023,"cited_by_count":30},{"year":2022,"cited_by_count":22},{"year":2021,"cited_by_count":21},{"year":2020,"cited_by_count":31},{"year":2019,"cited_by_count":24},{"year":2018,"cited_by_count":17},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":18},{"year":2015,"cited_by_count":17},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
