{"id":"https://openalex.org/W2797527938","doi":"https://doi.org/10.1007/s10589-018-0031-1","title":"Proximal primal\u2013dual best approximation algorithm with memory","display_name":"Proximal primal\u2013dual best approximation algorithm with memory","publication_year":2018,"publication_date":"2018-08-27","ids":{"openalex":"https://openalex.org/W2797527938","doi":"https://doi.org/10.1007/s10589-018-0031-1","mag":"2797527938"},"language":"en","primary_location":{"id":"doi:10.1007/s10589-018-0031-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-018-0031-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-018-0031-1.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10589-018-0031-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023952883","display_name":"Ewa M. Bednarczuk","orcid":"https://orcid.org/0000-0003-3683-6881"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]},{"id":"https://openalex.org/I66083562","display_name":"Systems Research Institute","ror":"https://ror.org/0111cp837","country_code":"PL","type":"facility","lineage":["https://openalex.org/I66083562","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"E. M. Bednarczuk","raw_affiliation_strings":["Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland","Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland","institution_ids":["https://openalex.org/I108403487"]},{"raw_affiliation_string":"Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086251368","display_name":"Anna Jezierska","orcid":"https://orcid.org/0000-0001-8235-7641"},"institutions":[{"id":"https://openalex.org/I169333911","display_name":"Gda\u0144sk University of Technology","ror":"https://ror.org/006x4sc24","country_code":"PL","type":"education","lineage":["https://openalex.org/I169333911"]},{"id":"https://openalex.org/I66083562","display_name":"Systems Research Institute","ror":"https://ror.org/0111cp837","country_code":"PL","type":"facility","lineage":["https://openalex.org/I66083562","https://openalex.org/I99542240"]},{"id":"https://openalex.org/I99542240","display_name":"Polish Academy of Sciences","ror":"https://ror.org/01dr6c206","country_code":"PL","type":"government","lineage":["https://openalex.org/I99542240"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"A. Jezierska","raw_affiliation_strings":["Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Gda\u0144sk, Poland","Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Gda\u0144sk, Poland","institution_ids":["https://openalex.org/I169333911"]},{"raw_affiliation_string":"Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland","institution_ids":["https://openalex.org/I66083562","https://openalex.org/I99542240"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034513876","display_name":"Krzysztof E. Rutkowski","orcid":"https://orcid.org/0000-0002-2626-2469"},"institutions":[{"id":"https://openalex.org/I108403487","display_name":"Warsaw University of Technology","ror":"https://ror.org/00y0xnp53","country_code":"PL","type":"education","lineage":["https://openalex.org/I108403487"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"K. E. Rutkowski","raw_affiliation_strings":["Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Information Science, Warsaw University of Technology, Warsaw, Poland","institution_ids":["https://openalex.org/I108403487"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5034513876"],"corresponding_institution_ids":["https://openalex.org/I108403487"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.03768648,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"71","issue":"3","first_page":"767","last_page":"794"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9990000128746033,"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":0.9948999881744385,"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":0.7176706790924072},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6744579076766968},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5304925441741943},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5289238691329956},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5280200839042664},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5088810920715332},{"id":"https://openalex.org/keywords/current","display_name":"Current (fluid)","score":0.44550222158432007},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.442065566778183},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37961599230766296},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3285433053970337},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.123257577419281},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08737942576408386}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7176706790924072},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6744579076766968},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5304925441741943},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5289238691329956},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5280200839042664},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5088810920715332},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.44550222158432007},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.442065566778183},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37961599230766296},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3285433053970337},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.123257577419281},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08737942576408386},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10589-018-0031-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-018-0031-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-018-0031-1.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:coopap:v:71:y:2018:i:3:d:10.1007_s10589-018-0031-1","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10589-018-0031-1","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"}],"best_oa_location":{"id":"doi:10.1007/s10589-018-0031-1","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10589-018-0031-1","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10589-018-0031-1.pdf","source":{"id":"https://openalex.org/S39243548","display_name":"Computational Optimization and Applications","issn_l":"0926-6003","issn":["0926-6003","1573-2894"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Optimization and Applications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2797527938.pdf","grobid_xml":"https://content.openalex.org/works/W2797527938.grobid-xml"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W199410564","https://openalex.org/W205960364","https://openalex.org/W407999889","https://openalex.org/W431540916","https://openalex.org/W604355987","https://openalex.org/W1495915592","https://openalex.org/W1512478894","https://openalex.org/W1548966286","https://openalex.org/W1560858410","https://openalex.org/W1767939703","https://openalex.org/W1850691639","https://openalex.org/W1869605349","https://openalex.org/W1922442141","https://openalex.org/W1965650079","https://openalex.org/W1975253701","https://openalex.org/W1984481261","https://openalex.org/W1989464734","https://openalex.org/W1993880409","https://openalex.org/W2000462146","https://openalex.org/W2007437458","https://openalex.org/W2016503956","https://openalex.org/W2019437904","https://openalex.org/W2039151776","https://openalex.org/W2047515743","https://openalex.org/W2048408528","https://openalex.org/W2051579945","https://openalex.org/W2059189829","https://openalex.org/W2061334381","https://openalex.org/W2062184313","https://openalex.org/W2065495103","https://openalex.org/W2066356711","https://openalex.org/W2077428669","https://openalex.org/W2078665452","https://openalex.org/W2079728872","https://openalex.org/W2095980290","https://openalex.org/W2097633811","https://openalex.org/W2103559027","https://openalex.org/W2112642314","https://openalex.org/W2154319048","https://openalex.org/W2182007996","https://openalex.org/W2182968499","https://openalex.org/W2241435520","https://openalex.org/W2254152852","https://openalex.org/W2259139337","https://openalex.org/W2261580627","https://openalex.org/W2296319761","https://openalex.org/W2297927615","https://openalex.org/W2443846959","https://openalex.org/W2486484692","https://openalex.org/W2587595384","https://openalex.org/W2607024191","https://openalex.org/W2622705236","https://openalex.org/W2769562649","https://openalex.org/W3103793615","https://openalex.org/W3104896827","https://openalex.org/W3123649567","https://openalex.org/W4229650096","https://openalex.org/W4231248581","https://openalex.org/W4249667877","https://openalex.org/W4250589301"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W1980454230","https://openalex.org/W2024436902","https://openalex.org/W374487401"],"abstract_inverted_index":{"We":[0],"propose":[1],"a":[2],"new":[3],"modified":[4],"primal\u2013dual":[5,96],"proximal":[6,95],"best":[7,93],"approximation":[8,94],"method":[9,22],"for":[10,76],"solving":[11],"convex":[12],"not":[13],"necessarily":[14],"differentiable":[15],"optimization":[16],"problems.":[17],"The":[18,81],"novelty":[19],"of":[20,50,56,90,111,130],"the":[21,37,54,57,62,91,104,109,112,128,134],"relies":[23],"on":[24,53,123],"introducing":[25],"memory":[26,85,132],"by":[27],"taking":[28],"into":[29,133],"account":[30],"iterates":[31],"computed":[32],"in":[33,36],"previous":[34,63],"steps":[35],"formulas":[38],"defining":[39],"current":[40,58],"iterate.":[41],"To":[42,65],"this":[43],"end":[44],"we":[45,69,99],"consider":[46],"projections":[47,68],"onto":[48,78],"intersections":[49],"halfspaces":[51],"generated":[52],"basis":[55],"as":[59,61],"well":[60],"iterates.":[64],"calculate":[66],"these":[67],"are":[70],"using":[71],"recently":[72],"obtained":[73],"closed-form":[74],"expressions":[75],"projectors":[77],"polyhedral":[79],"sets.":[80],"resulting":[82],"algorithm":[83,102],"with":[84,103,108],"inherits":[86],"strong":[87],"convergence":[88],"properties":[89],"original":[92,105,135],"algorithm.":[97,136],"Additionally,":[98],"compare":[100],"our":[101],"(non-inertial)":[106],"one":[107],"help":[110],"so":[113],"called":[114],"attraction":[115],"property":[116],"defined":[117],"below.":[118],"Extensive":[119],"numerical":[120],"experimental":[121],"results":[122],"image":[124],"reconstruction":[125],"problems":[126],"illustrate":[127],"advantages":[129],"including":[131]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
