{"id":"https://openalex.org/W2885948883","doi":"https://doi.org/10.1007/s10957-018-1369-3","title":"Inertial Forward\u2013Backward Algorithms with Perturbations: Application to Tikhonov Regularization","display_name":"Inertial Forward\u2013Backward Algorithms with Perturbations: Application to Tikhonov Regularization","publication_year":2018,"publication_date":"2018-08-09","ids":{"openalex":"https://openalex.org/W2885948883","doi":"https://doi.org/10.1007/s10957-018-1369-3","mag":"2885948883"},"language":"en","primary_location":{"id":"doi:10.1007/s10957-018-1369-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-018-1369-3","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","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/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"]},{"id":"https://openalex.org/I4210142014","display_name":"Institut Montpelli\u00e9rain Alexander Grothendieck","ror":"https://ror.org/044kxby82","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210141950","https://openalex.org/I4210142014"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Hedy Attouch","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques, IMAG, UMR CNRS 5149, Univ Montpellier, 34095, Montpellier Cedex 5, France","IMAG - Institut Montpelli\u00e9rain Alexander Grothendieck (UMR CNRS 5149 - Universit\u00e9 Montpellier 2, Case courrier 051, 34095 Montpellier cedex 5 - France - France)"],"raw_orcid":"https://orcid.org/0000-0003-2676-0887","affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, IMAG, UMR CNRS 5149, Univ Montpellier, 34095, Montpellier Cedex 5, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210142014"]},{"raw_affiliation_string":"IMAG - Institut Montpelli\u00e9rain Alexander Grothendieck (UMR CNRS 5149 - Universit\u00e9 Montpellier 2, Case courrier 051, 34095 Montpellier cedex 5 - France - France)","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110183023","display_name":"Alexandre Cabot","orcid":null},"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/I177064439","display_name":"Universit\u00e9 de Bourgogne","ror":"https://ror.org/03k1bsr36","country_code":"FR","type":"education","lineage":["https://openalex.org/I177064439"]},{"id":"https://openalex.org/I4210112333","display_name":"Institut de Math\u00e9matiques de Bourgogne","ror":"https://ror.org/021f0sa24","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210112333","https://openalex.org/I4405253280"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Cabot","raw_affiliation_strings":["Institut de Math\u00e9matiques de Bourgogne, UMR 5584, CNRS, Univ. Bourgogne Franche-Comt\u00e9, 21000, Dijon, France","IMB - Institut de Math\u00e9matiques de Bourgogne [Dijon] (Universit\u00e9 de Bourgogne - 9, avenue Alain Savary - B.P. 47 870 - 21078 Dijon Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Bourgogne, UMR 5584, CNRS, Univ. Bourgogne Franche-Comt\u00e9, 21000, Dijon, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210112333"]},{"raw_affiliation_string":"IMB - Institut de Math\u00e9matiques de Bourgogne [Dijon] (Universit\u00e9 de Bourgogne - 9, avenue Alain Savary - B.P. 47 870 - 21078 Dijon Cedex - France)","institution_ids":["https://openalex.org/I177064439","https://openalex.org/I4210112333"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025710979","display_name":"Zaki Chbani","orcid":"https://orcid.org/0000-0001-9054-8421"},"institutions":[{"id":"https://openalex.org/I119856527","display_name":"Cadi Ayyad University","ror":"https://ror.org/04xf6nm78","country_code":"MA","type":"education","lineage":["https://openalex.org/I119856527"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Zaki Chbani","raw_affiliation_strings":["Faculty of Sciences Semlalia, Mathematics, Cadi Ayyad University, 40000, Marrakech, Morocco","Department of Mathematics, Faculty of Sciences Semlalia (Cadi Ayyad University, P.O. Box 2390, Marrakech - Morocco)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Sciences Semlalia, Mathematics, Cadi Ayyad University, 40000, Marrakech, Morocco","institution_ids":["https://openalex.org/I119856527"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences Semlalia (Cadi Ayyad University, P.O. Box 2390, Marrakech - Morocco)","institution_ids":["https://openalex.org/I119856527"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022578878","display_name":"Hassan Riahi","orcid":"https://orcid.org/0000-0001-6248-1266"},"institutions":[{"id":"https://openalex.org/I119856527","display_name":"Cadi Ayyad University","ror":"https://ror.org/04xf6nm78","country_code":"MA","type":"education","lineage":["https://openalex.org/I119856527"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Hassan Riahi","raw_affiliation_strings":["Faculty of Sciences Semlalia, Mathematics, Cadi Ayyad University, 40000, Marrakech, Morocco","Department of Mathematics, Faculty of Sciences Semlalia (Cadi Ayyad University, P.O. Box 2390, Marrakech - Morocco)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Sciences Semlalia, Mathematics, Cadi Ayyad University, 40000, Marrakech, Morocco","institution_ids":["https://openalex.org/I119856527"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences Semlalia (Cadi Ayyad University, P.O. Box 2390, Marrakech - Morocco)","institution_ids":["https://openalex.org/I119856527"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5038818485"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307","https://openalex.org/I4210142014"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":5.0287,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.96631367,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"179","issue":"1","first_page":"1","last_page":"36"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9991000294685364,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9926999807357788,"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":0.7829070091247559},{"id":"https://openalex.org/keywords/tikhonov-regularization","display_name":"Tikhonov regularization","score":0.7683233022689819},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.6812127828598022},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.6140254139900208},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5209978222846985},{"id":"https://openalex.org/keywords/proximal-gradient-methods-for-learning","display_name":"Proximal gradient methods for learning","score":0.4954007863998413},{"id":"https://openalex.org/keywords/inertial-frame-of-reference","display_name":"Inertial frame of reference","score":0.49539220333099365},{"id":"https://openalex.org/keywords/backus\u2013gilbert-method","display_name":"Backus\u2013Gilbert method","score":0.4878106415271759},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.4771135151386261},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47247833013534546},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.4690079391002655},{"id":"https://openalex.org/keywords/regularization-perspectives-on-support-vector-machines","display_name":"Regularization perspectives on support vector machines","score":0.4617841839790344},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.46113598346710205},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42687657475471497},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4135967493057251},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.41250959038734436},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37744274735450745},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3109581470489502},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.20983931422233582},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.144525408744812},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09100028872489929}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7829070091247559},{"id":"https://openalex.org/C152442038","wikidata":"https://www.wikidata.org/wiki/Q2778212","display_name":"Tikhonov regularization","level":3,"score":0.7683233022689819},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.6812127828598022},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.6140254139900208},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5209978222846985},{"id":"https://openalex.org/C79248915","wikidata":"https://www.wikidata.org/wiki/Q17086776","display_name":"Proximal gradient methods for learning","level":5,"score":0.4954007863998413},{"id":"https://openalex.org/C173386949","wikidata":"https://www.wikidata.org/wiki/Q192735","display_name":"Inertial frame of reference","level":2,"score":0.49539220333099365},{"id":"https://openalex.org/C27872270","wikidata":"https://www.wikidata.org/wiki/Q4839810","display_name":"Backus\u2013Gilbert method","level":5,"score":0.4878106415271759},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.4771135151386261},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47247833013534546},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.4690079391002655},{"id":"https://openalex.org/C141718189","wikidata":"https://www.wikidata.org/wiki/Q7309628","display_name":"Regularization perspectives on support vector machines","level":4,"score":0.4617841839790344},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.46113598346710205},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42687657475471497},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4135967493057251},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.41250959038734436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37744274735450745},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3109581470489502},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.20983931422233582},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.144525408744812},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09100028872489929},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10957-018-1369-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10957-018-1369-3","pdf_url":null,"source":{"id":"https://openalex.org/S52430896","display_name":"Journal of Optimization Theory and Applications","issn_l":"0022-3239","issn":["0022-3239","1573-2878"],"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":"Journal of Optimization Theory and Applications","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01996816v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01996816","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Optimization Theory and Applications, 2018, 179 (1), pp.1-36. &#x27E8;10.1007/s10957-018-1369-3&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:RePEc:spr:joptap:v:179:y:2018:i:1:d:10.1007_s10957-018-1369-3","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10957-018-1369-3","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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W199410564","https://openalex.org/W202170286","https://openalex.org/W205960364","https://openalex.org/W320808933","https://openalex.org/W322738573","https://openalex.org/W597610935","https://openalex.org/W1506859583","https://openalex.org/W1547678669","https://openalex.org/W1568288633","https://openalex.org/W1837565340","https://openalex.org/W1946620893","https://openalex.org/W1968699683","https://openalex.org/W1989166601","https://openalex.org/W2005833769","https://openalex.org/W2006262045","https://openalex.org/W2014746566","https://openalex.org/W2019613464","https://openalex.org/W2019786292","https://openalex.org/W2028739379","https://openalex.org/W2038497950","https://openalex.org/W2053487511","https://openalex.org/W2063357812","https://openalex.org/W2077726563","https://openalex.org/W2095980290","https://openalex.org/W2100556411","https://openalex.org/W2124541940","https://openalex.org/W2176777789","https://openalex.org/W2302721240","https://openalex.org/W2326806701","https://openalex.org/W2490794238","https://openalex.org/W2528062157","https://openalex.org/W2610811713","https://openalex.org/W2731666329","https://openalex.org/W2735979640","https://openalex.org/W2759432802","https://openalex.org/W2913535645","https://openalex.org/W2952975724","https://openalex.org/W2963022670","https://openalex.org/W2964018031","https://openalex.org/W2964094444","https://openalex.org/W2964153427","https://openalex.org/W3100706439","https://openalex.org/W3123649567","https://openalex.org/W3141595720","https://openalex.org/W4229650096"],"related_works":["https://openalex.org/W2807240017","https://openalex.org/W2366023887","https://openalex.org/W2805921369","https://openalex.org/W2394283419","https://openalex.org/W2676810451","https://openalex.org/W2188929001","https://openalex.org/W2606473771","https://openalex.org/W3022004076","https://openalex.org/W2020486201","https://openalex.org/W2111475863"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":1}],"updated_date":"2026-08-14T07:06:38.338062","created_date":"2025-10-10T00:00:00"}
