{"id":"https://openalex.org/W2009467175","doi":"https://doi.org/10.1155/2009/691952","title":"Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis","display_name":"Relatively Inexact Proximal Point Algorithm and Linear Convergence Analysis","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2009467175","doi":"https://doi.org/10.1155/2009/691952","mag":"2009467175"},"language":"en","primary_location":{"id":"doi:10.1155/2009/691952","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2009/691952","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2009/691952.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"http://downloads.hindawi.com/journals/ijmms/2009/691952.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109972854","display_name":"Ram U. Verma","orcid":null},"institutions":[{"id":"https://openalex.org/I106959904","display_name":"Florida Institute of Technology","ror":"https://ror.org/04atsbb87","country_code":"US","type":"education","lineage":["https://openalex.org/I106959904"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ram U. Verma","raw_affiliation_strings":["Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA","Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA","institution_ids":["https://openalex.org/I106959904"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901","institution_ids":["https://openalex.org/I106959904"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109972854"],"corresponding_institution_ids":["https://openalex.org/I106959904"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.3472,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.59943047,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2009","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9983999729156494,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9937999844551086,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8832180500030518},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7163848876953125},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6539285182952881},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6418126821517944},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6007323861122131},{"id":"https://openalex.org/keywords/modes-of-convergence","display_name":"Modes of convergence (annotated index)","score":0.46733057498931885},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4638049602508545},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.45073288679122925},{"id":"https://openalex.org/keywords/compact-convergence","display_name":"Compact convergence","score":0.4480587840080261},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.43816906213760376},{"id":"https://openalex.org/keywords/normal-convergence","display_name":"Normal convergence","score":0.43622469902038574},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"Weak convergence","score":0.4357697367668152},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3814726769924164},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35424739122390747},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3112982511520386},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.257705956697464},{"id":"https://openalex.org/keywords/isolated-point","display_name":"Isolated point","score":0.14232590794563293},{"id":"https://openalex.org/keywords/topological-space","display_name":"Topological space","score":0.07747626304626465},{"id":"https://openalex.org/keywords/topological-vector-space","display_name":"Topological vector space","score":0.06947839260101318},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06481194496154785},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06314140558242798}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8832180500030518},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7163848876953125},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6539285182952881},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6418126821517944},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6007323861122131},{"id":"https://openalex.org/C48216909","wikidata":"https://www.wikidata.org/wiki/Q6889156","display_name":"Modes of convergence (annotated index)","level":5,"score":0.46733057498931885},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4638049602508545},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.45073288679122925},{"id":"https://openalex.org/C5871375","wikidata":"https://www.wikidata.org/wiki/Q1780715","display_name":"Compact convergence","level":4,"score":0.4480587840080261},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.43816906213760376},{"id":"https://openalex.org/C14928880","wikidata":"https://www.wikidata.org/wiki/Q1512559","display_name":"Normal convergence","level":4,"score":0.43622469902038574},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.4357697367668152},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3814726769924164},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35424739122390747},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3112982511520386},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.257705956697464},{"id":"https://openalex.org/C174265945","wikidata":"https://www.wikidata.org/wiki/Q1142889","display_name":"Isolated point","level":4,"score":0.14232590794563293},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.07747626304626465},{"id":"https://openalex.org/C47776270","wikidata":"https://www.wikidata.org/wiki/Q1455249","display_name":"Topological vector space","level":3,"score":0.06947839260101318},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06481194496154785},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06314140558242798},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C76178495","wikidata":"https://www.wikidata.org/wiki/Q4808784","display_name":"Asset (computer security)","level":2,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/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}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2009/691952","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2009/691952","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2009/691952.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:691952","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2009/691952.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:a7c64c085f50408885e7b17808308927","is_oa":true,"landing_page_url":"https://doaj.org/article/a7c64c085f50408885e7b17808308927","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2009 (2009)","raw_type":"article"},{"id":"pmh:oai:hindawi.com:10.1155/2009/691952","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2009/691952","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Research Article"}],"best_oa_location":{"id":"doi:10.1155/2009/691952","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2009/691952","pdf_url":"http://downloads.hindawi.com/journals/ijmms/2009/691952.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2009467175.pdf","grobid_xml":"https://content.openalex.org/works/W2009467175.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W111414977","https://openalex.org/W622837943","https://openalex.org/W639834748","https://openalex.org/W1547403762","https://openalex.org/W1972137641","https://openalex.org/W1979363840","https://openalex.org/W1990951140","https://openalex.org/W1993305160","https://openalex.org/W1994056204","https://openalex.org/W2038497950","https://openalex.org/W2072985063","https://openalex.org/W2092185228","https://openalex.org/W2116174279","https://openalex.org/W2135779729","https://openalex.org/W2582171088","https://openalex.org/W2594169092","https://openalex.org/W4235485079","https://openalex.org/W4251401614"],"related_works":["https://openalex.org/W2034145661","https://openalex.org/W2482464444","https://openalex.org/W2028595206","https://openalex.org/W576291453","https://openalex.org/W4253827225","https://openalex.org/W53647575","https://openalex.org/W2246194234","https://openalex.org/W1985261949","https://openalex.org/W2060982220","https://openalex.org/W2102183453"],"abstract_inverted_index":{"Based":[0],"on":[1,30,47],"a":[2,17,39],"notion":[3],"of":[4,16,20,57,61,70,73],"relatively":[5],"maximal":[6],"(":[7],"m":[8],")\u2010":[9],"relaxed":[10],"monotonicity":[11],",":[12],"the":[13,34,58,65,71,74,86],"approximation":[14],"solvability":[15],"general":[18],"class":[19],"inclusion":[21],"problems":[22],"is":[23,51,77],"discussed,":[24],"while":[25],"generalizing":[26],"Rockafellar\u2032s":[27],"theorem":[28],"(1976)":[29],"linear":[31],"convergence":[32],"using":[33],"proximal":[35],"point":[36],"algorithm":[37],"in":[38,63,90],"real":[40],"Hilbert":[41],"space":[42],"setting.":[43],"Convergence":[44],"analysis,":[45],"based":[46],"this":[48],"new":[49],"model,":[50],"simpler":[52],"and":[53],"compact":[54],"than":[55],"that":[56],"celebrated":[59],"technique":[60],"Rockafellar":[62],"which":[64],"Lipschitz":[66],"continuity":[67],"at":[68],"0":[69],"inverse":[72],"set\u2010valued":[75],"mapping":[76],"applied.":[78],"Furthermore,":[79],"it":[80],"can":[81,92],"be":[82,93],"used":[83],"to":[84,95],"generalize":[85],"Yosida":[87],"approximation,":[88],"which,":[89],"turn,":[91],"applied":[94],"first\u2010order":[96],"evolution":[97,102],"equations":[98],"as":[99,101],"well":[100],"inclusions.":[103]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}