{"id":"https://openalex.org/W2078853581","doi":"https://doi.org/10.1007/s10107-007-0133-5","title":"On the convergence of the proximal algorithm for nonsmooth functions involving analytic features","display_name":"On the convergence of the proximal algorithm for nonsmooth functions involving analytic features","publication_year":2007,"publication_date":"2007-05-03","ids":{"openalex":"https://openalex.org/W2078853581","doi":"https://doi.org/10.1007/s10107-007-0133-5","mag":"2078853581"},"language":"en","primary_location":{"id":"doi:10.1007/s10107-007-0133-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-007-0133-5","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00803898","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038818485","display_name":"H\u00e9dy Attouch","orcid":"https://orcid.org/0000-0003-2676-0887"},"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/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":true,"raw_author_name":"Hedy Attouch","raw_affiliation_strings":["I3M UMR CNRS 5149, Universit\u00e9 Montpellier II, Place Eug\u00e8ne Bataillon, 34095, Montpellier, France","Universit\u00e9 Montpellier II, I3M UMR CNRS 5149, Place Eug\u00e8ne Bataillon, 34095, Montpellier, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"I3M UMR CNRS 5149, Universit\u00e9 Montpellier II, Place Eug\u00e8ne Bataillon, 34095, Montpellier, France","institution_ids":["https://openalex.org/I19894307","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Universit\u00e9 Montpellier II, I3M UMR CNRS 5149, Place Eug\u00e8ne Bataillon, 34095, Montpellier, France#TAB#","institution_ids":["https://openalex.org/I19894307","https://openalex.org/I1294671590"]}]},{"author_position":"last","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/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J\u00e9r\u00f4me Bolte","raw_affiliation_strings":["Equipe Combinatoire et Optimisation (UMR 7090), Case 189, Universit\u00e9 Pierre et Marie Curie, 4 Place Jussieu, 75252, Paris Cedex 05, France","Universit\u00e9 Pierre et Marie Curie, Equipe Combinatoire et Optimisation (UMR 7090), Case 189, 4 Place Jussieu, 75252, Paris Cedex 05, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equipe Combinatoire et Optimisation (UMR 7090), Case 189, Universit\u00e9 Pierre et Marie Curie, 4 Place Jussieu, 75252, Paris Cedex 05, France","institution_ids":["https://openalex.org/I39804081"]},{"raw_affiliation_string":"Universit\u00e9 Pierre et Marie Curie, Equipe Combinatoire et Optimisation (UMR 7090), Case 189, 4 Place Jussieu, 75252, Paris Cedex 05, France#TAB#","institution_ids":["https://openalex.org/I39804081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038818485"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307"],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":4.4929,"has_fulltext":false,"cited_by_count":601,"citation_normalized_percentile":{"value":0.94540276,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"116","issue":"1-2","first_page":"5","last_page":"16"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9990000128746033,"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":0.9990000128746033,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9908999800682068,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8869187831878662},{"id":"https://openalex.org/keywords/flatness","display_name":"Flatness (cosmology)","score":0.7100390195846558},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6698180437088013},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5728256702423096},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.509252667427063},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.49779248237609863},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.45140206813812256},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36125099658966064},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36028262972831726},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3579365313053131},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.054413020610809326}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8869187831878662},{"id":"https://openalex.org/C2778530986","wikidata":"https://www.wikidata.org/wiki/Q5457948","display_name":"Flatness (cosmology)","level":3,"score":0.7100390195846558},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6698180437088013},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5728256702423096},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.509252667427063},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.49779248237609863},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.45140206813812256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36125099658966064},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36028262972831726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3579365313053131},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.054413020610809326},{"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/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"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/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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10107-007-0133-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10107-007-0133-5","pdf_url":null,"source":{"id":"https://openalex.org/S193920097","display_name":"Mathematical Programming","issn_l":"0025-5610","issn":["0025-5610","1436-4646"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Programming","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-00803898v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00803898","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":"Mathematical Programming, 2007, 116 (1), pp.5-16. &#x27E8;10.1007/s10107-007-0133-5&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:publications.ut-capitole.fr:3428","is_oa":false,"landing_page_url":"http://tse-fr.eu/pub/23251","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":{"id":"pmh:oai:HAL:hal-00803898v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00803898","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":"Mathematical Programming, 2007, 116 (1), pp.5-16. &#x27E8;10.1007/s10107-007-0133-5&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5799999833106995}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W26023427","https://openalex.org/W48894704","https://openalex.org/W97027186","https://openalex.org/W199410564","https://openalex.org/W1485995001","https://openalex.org/W1512226162","https://openalex.org/W1539838732","https://openalex.org/W1608145022","https://openalex.org/W1787101211","https://openalex.org/W1960239420","https://openalex.org/W1970033879","https://openalex.org/W1996195522","https://openalex.org/W2021361347","https://openalex.org/W2022541060","https://openalex.org/W2027239288","https://openalex.org/W2029465407","https://openalex.org/W2031529027","https://openalex.org/W2064011783","https://openalex.org/W2070997813","https://openalex.org/W2072643460","https://openalex.org/W2076858541","https://openalex.org/W2077612096","https://openalex.org/W2079004067","https://openalex.org/W2135779729","https://openalex.org/W2153562582","https://openalex.org/W2329975073","https://openalex.org/W2331639718","https://openalex.org/W2543381247","https://openalex.org/W2955892489","https://openalex.org/W3043060850","https://openalex.org/W4210605524","https://openalex.org/W4249513058","https://openalex.org/W4285719527","https://openalex.org/W4298032328","https://openalex.org/W4299599836"],"related_works":["https://openalex.org/W2789295429","https://openalex.org/W2066314436","https://openalex.org/W2733767282","https://openalex.org/W2510927817","https://openalex.org/W2540573954","https://openalex.org/W2743501974","https://openalex.org/W2782313579","https://openalex.org/W2588834286","https://openalex.org/W2508288055","https://openalex.org/W2359588980"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":18},{"year":2025,"cited_by_count":50},{"year":2024,"cited_by_count":48},{"year":2023,"cited_by_count":46},{"year":2022,"cited_by_count":44},{"year":2021,"cited_by_count":76},{"year":2020,"cited_by_count":64},{"year":2019,"cited_by_count":52},{"year":2018,"cited_by_count":41},{"year":2017,"cited_by_count":37},{"year":2016,"cited_by_count":41},{"year":2015,"cited_by_count":20},{"year":2014,"cited_by_count":24},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-23T13:55:30.953635","created_date":"2025-10-10T00:00:00"}
