{"id":"https://openalex.org/W3020799108","doi":"https://doi.org/10.1007/s11590-020-01580-5","title":"Regularization projection method for solving bilevel variational inequality problem","display_name":"Regularization projection method for solving bilevel variational inequality problem","publication_year":2020,"publication_date":"2020-04-25","ids":{"openalex":"https://openalex.org/W3020799108","doi":"https://doi.org/10.1007/s11590-020-01580-5","mag":"3020799108"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-020-01580-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-020-01580-5","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","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/A5002646790","display_name":"Dang Van Hieu","orcid":"https://orcid.org/0000-0002-5195-1637"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Dang Van Hieu","raw_affiliation_strings":["Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033131577","display_name":"Abdellatif Moudafi","orcid":null},"institutions":[{"id":"https://openalex.org/I21491767","display_name":"Aix-Marseille Universit\u00e9","ror":"https://ror.org/035xkbk20","country_code":"FR","type":"education","lineage":["https://openalex.org/I21491767"]},{"id":"https://openalex.org/I4210114274","display_name":"Laboratoire d\u2019Informatique et Syst\u00e8mes","ror":"https://ror.org/0257sgk90","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I143002897","https://openalex.org/I21491767","https://openalex.org/I4210114274"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Abdellatif Moudafi","raw_affiliation_strings":["Aix-Marseille Universit\u00e9, LIS UMR CNRS 7020, Marseille, France","I&M - Images et Mod\u00e8les (France)","LSIS - Laboratoire des Sciences de l'Information et des Syst\u00e8mes (Domaine Universitaire de Saint-J\u00e9r\u00f4me\r\nBatiment Polytech\r\nAvenue Escadrille Normandie-Niemen\r\n13397 MARSEILLE CEDEX 20 - France)","LIS - Laboratoire d'Informatique et des Syst\u00e8mes (LIS) (Marseille, Toulon) (Aix Marseille Universit\u00e9 \u2013 Campus de Saint J\u00e9r\u00f4me \u2013 Bat. Polytech, 52 Av. Escadrille Normandie Niemen, 13397 Marseille Cedex 20 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Aix-Marseille Universit\u00e9, LIS UMR CNRS 7020, Marseille, France","institution_ids":["https://openalex.org/I21491767","https://openalex.org/I4210114274","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"I&M - Images et Mod\u00e8les (France)","institution_ids":[]},{"raw_affiliation_string":"LSIS - Laboratoire des Sciences de l'Information et des Syst\u00e8mes (Domaine Universitaire de Saint-J\u00e9r\u00f4me\r\nBatiment Polytech\r\nAvenue Escadrille Normandie-Niemen\r\n13397 MARSEILLE CEDEX 20 - France)","institution_ids":["https://openalex.org/I4210114274"]},{"raw_affiliation_string":"LIS - Laboratoire d'Informatique et des Syst\u00e8mes (LIS) (Marseille, Toulon) (Aix Marseille Universit\u00e9 \u2013 Campus de Saint J\u00e9r\u00f4me \u2013 Bat. Polytech, 52 Av. Escadrille Normandie Niemen, 13397 Marseille Cedex 20 - France)","institution_ids":["https://openalex.org/I4210114274","https://openalex.org/I21491767"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002646790"],"corresponding_institution_ids":["https://openalex.org/I141445968"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.7673,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.92250184,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"15","issue":"1","first_page":"205","last_page":"229"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.989300012588501,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9829000234603882,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/subgradient-method","display_name":"Subgradient method","score":0.918717622756958},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.839336097240448},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.7939294576644897},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6984567642211914},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6528042554855347},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.6088941097259521},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6074566841125488},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5957109928131104},{"id":"https://openalex.org/keywords/strongly-monotone","display_name":"Strongly monotone","score":0.5426493287086487},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.5133325457572937},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.5075327157974243},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4908626675605774},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4589676856994629},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4343162775039673},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.41434958577156067},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39269953966140747},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3625338077545166},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.3165298104286194},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.2870669960975647},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16467395424842834},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12285393476486206}],"concepts":[{"id":"https://openalex.org/C158968445","wikidata":"https://www.wikidata.org/wiki/Q7631150","display_name":"Subgradient method","level":2,"score":0.918717622756958},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.839336097240448},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.7939294576644897},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6984567642211914},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6528042554855347},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.6088941097259521},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6074566841125488},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5957109928131104},{"id":"https://openalex.org/C12715386","wikidata":"https://www.wikidata.org/wiki/Q7624691","display_name":"Strongly monotone","level":3,"score":0.5426493287086487},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.5133325457572937},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.5075327157974243},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4908626675605774},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4589676856994629},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4343162775039673},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.41434958577156067},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39269953966140747},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3625338077545166},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.3165298104286194},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2870669960975647},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16467395424842834},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12285393476486206},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11590-020-01580-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-020-01580-5","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02880723v1","is_oa":false,"landing_page_url":"https://amu.hal.science/hal-02880723","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":"Optimization Letters, 2020, 15 (1), pp.205-229. ⟨10.1007/s11590-020-01580-5⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.5699999928474426,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G6725076299","display_name":null,"funder_award_id":"101.01-2020.06","funder_id":"https://openalex.org/F4320309617","funder_display_name":"National Foundation for Science and Technology Development"}],"funders":[{"id":"https://openalex.org/F4320309617","display_name":"National Foundation for Science and Technology Development","ror":"https://ror.org/04rw64z44"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W12587253","https://openalex.org/W325445372","https://openalex.org/W605736217","https://openalex.org/W1516681311","https://openalex.org/W1519983590","https://openalex.org/W1543439990","https://openalex.org/W1546168022","https://openalex.org/W1588628884","https://openalex.org/W1978826935","https://openalex.org/W1991765628","https://openalex.org/W1998544309","https://openalex.org/W2003055811","https://openalex.org/W2015928709","https://openalex.org/W2021549982","https://openalex.org/W2055941941","https://openalex.org/W2069343783","https://openalex.org/W2069491950","https://openalex.org/W2078819283","https://openalex.org/W2081985785","https://openalex.org/W2099681657","https://openalex.org/W2169138342","https://openalex.org/W2254218369","https://openalex.org/W2284624424","https://openalex.org/W2435472869","https://openalex.org/W2443846959","https://openalex.org/W2499145065","https://openalex.org/W2740739160","https://openalex.org/W2751887966","https://openalex.org/W2803005800","https://openalex.org/W2811489376","https://openalex.org/W2885473730","https://openalex.org/W2904285751","https://openalex.org/W2907534917","https://openalex.org/W2933689882","https://openalex.org/W2945786968","https://openalex.org/W2950866122","https://openalex.org/W2953574340","https://openalex.org/W2963935887","https://openalex.org/W2979838783","https://openalex.org/W3013028485","https://openalex.org/W3015556107","https://openalex.org/W3099304089","https://openalex.org/W3101497372","https://openalex.org/W4301791716"],"related_works":["https://openalex.org/W2892725081","https://openalex.org/W4289490618","https://openalex.org/W2608242279","https://openalex.org/W2973499897","https://openalex.org/W3080884585","https://openalex.org/W2026392561","https://openalex.org/W1561297735","https://openalex.org/W4390862986","https://openalex.org/W2392510576","https://openalex.org/W2910556747"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-09T13:55:54.758798","created_date":"2025-10-10T00:00:00"}