{"id":"https://openalex.org/W3191040197","doi":"https://doi.org/10.1007/s10898-021-01067-2","title":"Strict directional solutions in vectorial problems: necessary optimality conditions","display_name":"Strict directional solutions in vectorial problems: necessary optimality conditions","publication_year":2021,"publication_date":"2021-07-29","ids":{"openalex":"https://openalex.org/W3191040197","doi":"https://doi.org/10.1007/s10898-021-01067-2","mag":"3191040197"},"language":"en","primary_location":{"id":"doi:10.1007/s10898-021-01067-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-021-01067-2","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global 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/A5101744853","display_name":"Mohamed Mansour","orcid":"https://orcid.org/0000-0002-3618-6543"},"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":"Mohamed Ait Mansour","raw_affiliation_strings":["D\u00e9partement de Physiques, LPFAS, Facult\u00e9 Polydisciplinaire, Universit\u00e9 Cadi Ayyad, Safi, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Physiques, LPFAS, Facult\u00e9 Polydisciplinaire, Universit\u00e9 Cadi Ayyad, Safi, Morocco","institution_ids":["https://openalex.org/I119856527"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071610741","display_name":"Marius Durea","orcid":"https://orcid.org/0000-0002-6429-0209"},"institutions":[{"id":"https://openalex.org/I138164181","display_name":"Alexandru Ioan Cuza University","ror":"https://ror.org/022kvet57","country_code":"RO","type":"education","lineage":["https://openalex.org/I138164181"]},{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Marius Durea","raw_affiliation_strings":["Faculty of Mathematics, \u201cAlexandru Ioan Cuza\u201d University, Bd. Carol I, nr. 11, 700506, Ia\u015fi, Romania","\u201cOctav Mayer\u201d Institute of Mathematics of the Romanian Academy, Ia\u015fi, Romania"],"raw_orcid":"https://orcid.org/0000-0002-6429-0209","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, \u201cAlexandru Ioan Cuza\u201d University, Bd. Carol I, nr. 11, 700506, Ia\u015fi, Romania","institution_ids":["https://openalex.org/I138164181"]},{"raw_affiliation_string":"\u201cOctav Mayer\u201d Institute of Mathematics of the Romanian Academy, Ia\u015fi, Romania","institution_ids":["https://openalex.org/I58077936"]}]},{"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":["D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences Semlalia, Laboratoire Math\u00e9matiques et Dynamique des Populations, Universit\u00e9 Cadi Ayyad, Marrakesh, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques, Facult\u00e9 des Sciences Semlalia, Laboratoire Math\u00e9matiques et Dynamique des Populations, Universit\u00e9 Cadi Ayyad, Marrakesh, Morocco","institution_ids":["https://openalex.org/I119856527"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071610741"],"corresponding_institution_ids":["https://openalex.org/I138164181","https://openalex.org/I58077936"],"apc_list":{"value":2780,"currency":"USD","value_usd":2780},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.14585186,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"82","issue":"1","first_page":"119","last_page":"138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":1.0,"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":1.0,"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":0.9980000257492065,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9825999736785889,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8647626042366028},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.7417848706245422},{"id":"https://openalex.org/keywords/directional-derivative","display_name":"Directional derivative","score":0.7332884669303894},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6964559555053711},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6171690821647644},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46905210614204407},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36329716444015503},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3239556849002838},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.12261047959327698},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11905071139335632},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08862000703811646}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8647626042366028},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7417848706245422},{"id":"https://openalex.org/C2011187","wikidata":"https://www.wikidata.org/wiki/Q383851","display_name":"Directional derivative","level":2,"score":0.7332884669303894},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6964559555053711},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6171690821647644},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46905210614204407},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36329716444015503},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3239556849002838},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.12261047959327698},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11905071139335632},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08862000703811646},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10898-021-01067-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10898-021-01067-2","pdf_url":null,"source":{"id":"https://openalex.org/S115925768","display_name":"Journal of Global Optimization","issn_l":"0925-5001","issn":["0925-5001","1573-2916"],"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 Global Optimization","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:jglopt:v:82:y:2022:i:1:d:10.1007_s10898-021-01067-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s10898-021-01067-2","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1582299569","https://openalex.org/W1967241387","https://openalex.org/W1984538196","https://openalex.org/W1995700855","https://openalex.org/W2009787992","https://openalex.org/W2027200819","https://openalex.org/W2036052184","https://openalex.org/W2056023144","https://openalex.org/W2057578212","https://openalex.org/W2063333239","https://openalex.org/W2064114733","https://openalex.org/W2067919445","https://openalex.org/W2153562582","https://openalex.org/W2529091809","https://openalex.org/W2964348151","https://openalex.org/W2999896881"],"related_works":["https://openalex.org/W1964872188","https://openalex.org/W2187391117","https://openalex.org/W1981809986","https://openalex.org/W2949367465","https://openalex.org/W2587048717","https://openalex.org/W4235203617","https://openalex.org/W2006359264","https://openalex.org/W2364963568","https://openalex.org/W4243698225","https://openalex.org/W2075869708"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
