{"id":"https://openalex.org/W2124125796","doi":"https://doi.org/10.1007/s101070050022","title":"Error bounds for proximal point subproblems and associated inexact proximal point algorithms","display_name":"Error bounds for proximal point subproblems and associated inexact proximal point algorithms","publication_year":2000,"publication_date":"2000-08-01","ids":{"openalex":"https://openalex.org/W2124125796","doi":"https://doi.org/10.1007/s101070050022","mag":"2124125796"},"language":"en","primary_location":{"id":"doi:10.1007/s101070050022","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s101070050022","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110039123","display_name":"M. V. Solodov","orcid":null},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]},{"id":"https://openalex.org/I4210128604","display_name":"Instituto de Pesquisas Jardim Bot\u00e2nico do Rio de Janeiro","ror":"https://ror.org/033xtdz52","country_code":"BR","type":"archive","lineage":["https://openalex.org/I4210128604"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"M.V. Solodov","raw_affiliation_strings":["Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ 22460-320, Brazil, e-mail: {solodov,benar}@impa.br, BR","Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ 22460-320, Brazil, e-mail: {solodov,benar}@impa.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ 22460-320, Brazil, e-mail: {solodov,benar}@impa.br, BR","institution_ids":["https://openalex.org/I141883831","https://openalex.org/I4210128604"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ 22460-320, Brazil, e-mail: {solodov,benar}@impa.br","institution_ids":["https://openalex.org/I141883831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053683082","display_name":"B. F. Svaiter","orcid":"https://orcid.org/0000-0003-3656-9883"},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]},{"id":"https://openalex.org/I4210128604","display_name":"Instituto de Pesquisas Jardim Bot\u00e2nico do Rio de Janeiro","ror":"https://ror.org/033xtdz52","country_code":"BR","type":"archive","lineage":["https://openalex.org/I4210128604"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"B.F. Svaiter","raw_affiliation_strings":["Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ 22460-320, Brazil, e-mail: {solodov,benar}@impa.br, BR","Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ 22460-320, Brazil, e-mail: {solodov,benar}@impa.br"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ 22460-320, Brazil, e-mail: {solodov,benar}@impa.br, BR","institution_ids":["https://openalex.org/I141883831","https://openalex.org/I4210128604"]},{"raw_affiliation_string":"Instituto de Matem\u00e1tica Pura e Aplicada, Estrada Dona Castorina 110, Jardim Bot\u00e2nico, Rio de Janeiro, RJ 22460-320, Brazil, e-mail: {solodov,benar}@impa.br","institution_ids":["https://openalex.org/I141883831"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2190,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":6.1059,"has_fulltext":false,"cited_by_count":101,"citation_normalized_percentile":{"value":0.96953603,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"88","issue":"2","first_page":"371","last_page":"389"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998000264167786,"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":0.9998000264167786,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9925000071525574,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9890999794006348,"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/mathematics","display_name":"Mathematics","score":0.7924737930297852},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6239228248596191},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6082982420921326},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5853268504142761},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.5817257165908813},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5442604422569275},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5378775596618652},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.48784518241882324},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44495242834091187},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.43505096435546875},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.42579177021980286},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41944289207458496},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.38692089915275574},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17192456126213074}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7924737930297852},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6239228248596191},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6082982420921326},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5853268504142761},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.5817257165908813},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5442604422569275},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5378775596618652},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.48784518241882324},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44495242834091187},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.43505096435546875},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.42579177021980286},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41944289207458496},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38692089915275574},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17192456126213074},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s101070050022","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s101070050022","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:CiteSeerX.psu:10.1.1.34.1313","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.1313","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.wisc.edu/~solodov/solsva00errb.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6200000047683716,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W25288802","https://openalex.org/W61552049","https://openalex.org/W128756787","https://openalex.org/W163258351","https://openalex.org/W202170286","https://openalex.org/W240703482","https://openalex.org/W257907672","https://openalex.org/W1484204181","https://openalex.org/W1545461878","https://openalex.org/W1564612581","https://openalex.org/W1575261714","https://openalex.org/W1969073096","https://openalex.org/W1969867455","https://openalex.org/W1972312845","https://openalex.org/W1977600144","https://openalex.org/W1982011875","https://openalex.org/W1985348591","https://openalex.org/W1993305160","https://openalex.org/W1995227244","https://openalex.org/W2008590178","https://openalex.org/W2022428742","https://openalex.org/W2023821846","https://openalex.org/W2037679050","https://openalex.org/W2038497950","https://openalex.org/W2055467852","https://openalex.org/W2058532290","https://openalex.org/W2065121429","https://openalex.org/W2082451773","https://openalex.org/W2093246563","https://openalex.org/W2107710567","https://openalex.org/W2132677982","https://openalex.org/W2135779729","https://openalex.org/W2138216979","https://openalex.org/W2141640731","https://openalex.org/W2156074207","https://openalex.org/W2160068964","https://openalex.org/W2186467072","https://openalex.org/W2485839250"],"related_works":["https://openalex.org/W1489292980","https://openalex.org/W2795079910","https://openalex.org/W2951610245","https://openalex.org/W3118444755","https://openalex.org/W3037410748","https://openalex.org/W1430963189","https://openalex.org/W1974262772","https://openalex.org/W2049901819","https://openalex.org/W2085771669","https://openalex.org/W2052430123"],"abstract_inverted_index":null,"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":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
