{"id":"https://openalex.org/W2726664478","doi":"https://doi.org/10.1137/16m1080896","title":"An Extended Fenchel--Lagrange Duality Approach and Optimality Conditions for Strong Bilevel Programming Problems","display_name":"An Extended Fenchel--Lagrange Duality Approach and Optimality Conditions for Strong Bilevel Programming Problems","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2726664478","doi":"https://doi.org/10.1137/16m1080896","mag":"2726664478"},"language":"en","primary_location":{"id":"doi:10.1137/16m1080896","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1080896","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","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/A5015474321","display_name":"Abdelmalek Aboussoror","orcid":null},"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":true,"raw_author_name":"A. Aboussoror","raw_affiliation_strings":["Facult\u00e9 Polydisciplinaire de Safi, Laboratoire LMC (Universit\u00e9 Cadi Ayyad, B.P. 4162,\r\nSidi Bouzid, Safi, Morocco - Morocco)"],"affiliations":[{"raw_affiliation_string":"Facult\u00e9 Polydisciplinaire de Safi, Laboratoire LMC (Universit\u00e9 Cadi Ayyad, B.P. 4162,\r\nSidi Bouzid, Safi, Morocco - Morocco)","institution_ids":["https://openalex.org/I119856527"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018944126","display_name":"Samir Adly","orcid":"https://orcid.org/0000-0002-4375-0106"},"institutions":[{"id":"https://openalex.org/I4210093397","display_name":"XLIM","ror":"https://ror.org/00f7srh09","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I32881790","https://openalex.org/I4210093397","https://openalex.org/I4210095849","https://openalex.org/I65806277"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"S. Adly","raw_affiliation_strings":["XLIM-MATHIS - Math\u00e9matiques & S\u00e9curit\u00e9 de l'information (XLIM -  123, avenue Albert Thomas - 87060 LIMOGES CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"XLIM-MATHIS - Math\u00e9matiques & S\u00e9curit\u00e9 de l'information (XLIM -  123, avenue Albert Thomas - 87060 LIMOGES CEDEX - France)","institution_ids":["https://openalex.org/I4210093397"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109293369","display_name":"Fatima Ezzahra Saissi","orcid":null},"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":"F. E. Saissi","raw_affiliation_strings":["Facult\u00e9 Polydisciplinaire de Safi, Laboratoire LMC (Universit\u00e9 Cadi Ayyad, B.P. 4162,\r\nSidi Bouzid, Safi, Morocco - Morocco)"],"affiliations":[{"raw_affiliation_string":"Facult\u00e9 Polydisciplinaire de Safi, Laboratoire LMC (Universit\u00e9 Cadi Ayyad, B.P. 4162,\r\nSidi Bouzid, Safi, Morocco - Morocco)","institution_ids":["https://openalex.org/I119856527"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015474321"],"corresponding_institution_ids":["https://openalex.org/I119856527"],"apc_list":null,"apc_paid":null,"fwci":0.4542,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.64860764,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"27","issue":"2","first_page":"1230","last_page":"1255"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9995999932289124,"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":0.9995999932289124,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9343000054359436,"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/strong-duality","display_name":"Strong duality","score":0.8196818828582764},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.8085635304450989},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.745448112487793},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.6788234710693359},{"id":"https://openalex.org/keywords/bilevel-optimization","display_name":"Bilevel optimization","score":0.6779245734214783},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.6291671395301819},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6157832741737366},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.6080148220062256},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.5843337178230286},{"id":"https://openalex.org/keywords/perturbation-function","display_name":"Perturbation function","score":0.5326399803161621},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.48277798295021057},{"id":"https://openalex.org/keywords/fenchels-duality-theorem","display_name":"Fenchel's duality theorem","score":0.47457125782966614},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.46277081966400146},{"id":"https://openalex.org/keywords/interior-point-method","display_name":"Interior point method","score":0.4625268578529358},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.42390698194503784},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37480056285858154},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.28170037269592285},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2629745602607727},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.16033679246902466},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14449051022529602},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1393495798110962}],"concepts":[{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.8196818828582764},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.8085635304450989},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.745448112487793},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.6788234710693359},{"id":"https://openalex.org/C3309286","wikidata":"https://www.wikidata.org/wiki/Q4907693","display_name":"Bilevel optimization","level":3,"score":0.6779245734214783},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.6291671395301819},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6157832741737366},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.6080148220062256},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.5843337178230286},{"id":"https://openalex.org/C102144036","wikidata":"https://www.wikidata.org/wiki/Q7170952","display_name":"Perturbation function","level":5,"score":0.5326399803161621},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.48277798295021057},{"id":"https://openalex.org/C32580822","wikidata":"https://www.wikidata.org/wiki/Q5443003","display_name":"Fenchel's duality theorem","level":5,"score":0.47457125782966614},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.46277081966400146},{"id":"https://openalex.org/C155253501","wikidata":"https://www.wikidata.org/wiki/Q461992","display_name":"Interior point method","level":2,"score":0.4625268578529358},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.42390698194503784},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37480056285858154},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.28170037269592285},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2629745602607727},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.16033679246902466},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14449051022529602},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1393495798110962},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1080896","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1080896","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01656276v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01656276","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":"SIAM Journal on Optimization, 2017, 27 (2), pp.1230-1255. ⟨10.1137/16M1080896⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W79905171","https://openalex.org/W1980654449","https://openalex.org/W1990754283","https://openalex.org/W1994306362","https://openalex.org/W2000822214","https://openalex.org/W2016306996","https://openalex.org/W2019938296","https://openalex.org/W2027366985","https://openalex.org/W2028766715","https://openalex.org/W2040852176","https://openalex.org/W2042470984","https://openalex.org/W2053671651","https://openalex.org/W2056846819","https://openalex.org/W2087510134","https://openalex.org/W2325192077"],"related_works":["https://openalex.org/W1687657632","https://openalex.org/W4210245775","https://openalex.org/W2351130384","https://openalex.org/W4220928172","https://openalex.org/W3213165575","https://openalex.org/W2262421032","https://openalex.org/W4313014939","https://openalex.org/W2136200239","https://openalex.org/W1999755063","https://openalex.org/W2362763982"],"abstract_inverted_index":{"In":[0],"this":[1,59],"paper":[2],"we":[3,62],"give":[4],"a":[5,10,24,50,116],"conjugate":[6],"duality":[7,60,99],"approach":[8,17,91],"for":[9,69,81],"strong":[11,104],"bilevel":[12,105],"programming":[13,106],"problem":[14,27,40,84,120],"$(S)$.":[15,56,85],"The":[16],"is":[18,108,121],"based":[19],"on":[20],"the":[21,30,38,70,82,97,101,111],"use":[22],"of":[23,26,41,49,52,103],"regularization":[25],"$(S)$":[28,42],"and":[29,45,65,75],"so-called":[31],"Fenchel--Lagrange":[32,98],"duality.":[33],"We":[34,86],"first":[35],"show":[36],"that":[37,88],"regularized":[39,53,71],"admits":[43],"solutions":[44,54],"any":[46],"accumulation":[47],"point":[48],"sequence":[51],"solves":[55],"Then,":[57],"via":[58],"approach,":[61],"establish":[63],"necessary":[64,74],"sufficient":[66,76],"optimality":[67,77],"conditions":[68,78],"problem.":[72],"Finally,":[73],"are":[79],"given":[80],"initial":[83],"note":[87],"such":[89],"an":[90],"which":[92],"allows":[93],"us":[94],"to":[95,100,115],"apply":[96],"class":[102],"problems":[107],"new":[109],"in":[110],"literature.":[112],"An":[113],"application":[114],"two-level":[117],"resource":[118],"allocation":[119],"given.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}