{"id":"https://openalex.org/W1516639947","doi":"https://doi.org/10.52846/ami.v31i0.157","title":"A necessary optimality condition for quasiconvex functions on closed convex sets","display_name":"A necessary optimality condition for quasiconvex functions on closed convex sets","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W1516639947","doi":"https://doi.org/10.52846/ami.v31i0.157","mag":"1516639947"},"language":"en","primary_location":{"id":"pmh:oai:ami.inf.ucv.ro:article/157","doi":"https://doi.org/10.52846/ami.v31i0.157","is_oa":true,"landing_page_url":"http://inf.ucv.ro/~ami/index.php/ami/article/view/157","pdf_url":"http://inf.ucv.ro/~ami/index.php/ami/article/download/157/154","source":{"id":"https://openalex.org/S2764551600","display_name":"Annals of the University of Craiova Mathematics and Computer Science Series","issn_l":"1223-6934","issn":["1223-6934","2246-9958"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/I97553796","host_organization_name":"University of Craiova","host_organization_lineage":["https://openalex.org/I97553796"],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1223-6934","raw_type":"info:eu-repo/semantics/article"},"parent_works":[],"lineage":["https://openalex.org/W1516639947"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"http://inf.ucv.ro/~ami/index.php/ami/article/download/157/154","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077197197","display_name":"Abdessamad Jaddar","orcid":"https://orcid.org/0000-0001-6492-0920","observed_orcids":["https://orcid.org/0000-0001-6492-0920"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Jaddar","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-6492-0920","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5043583186","display_name":"Youssef Jabri","orcid":"https://orcid.org/0000-0002-2325-3196","observed_orcids":["https://orcid.org/0000-0002-2325-3196"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Youssef Jabri","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2325-3196","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":null,"first_page":"43","last_page":"46"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9994999766349792,"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":0.9994999766349792,"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":0.00019999999494757503,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.0,"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/quasiconvex-functions","display_name":"quasiconvex functions","score":0.9309999942779541},{"id":"https://openalex.org/keywords/necessary-optimality-conditions","display_name":"necessary optimality conditions","score":0.9229999780654907},{"id":"https://openalex.org/keywords/closed-convex-sets","display_name":"closed convex sets","score":0.7820000052452087},{"id":"https://openalex.org/keywords/minimization-problems","display_name":"minimization problems","score":0.722000002861023},{"id":"https://openalex.org/keywords/lower-semicontinuous-functions","display_name":"lower semicontinuous functions","score":0.9380000233650208},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"constrained optimization","score":0.6060000061988831}],"concepts":[{"id":"https://openalex.org/C80278974","wikidata":"https://www.wikidata.org/wiki/Q1126412","display_name":"Quasiconvex function","level":5,"score":0.9950689077377319},{"id":"https://openalex.org/C118888059","wikidata":"https://www.wikidata.org/wiki/Q7254692","display_name":"Pseudoconvex function","level":5,"score":0.7751980423927307},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.6329256296157837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6261551976203918},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.594959020614624},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.577348530292511},{"id":"https://openalex.org/C50862404","wikidata":"https://www.wikidata.org/wiki/Q3075259","display_name":"Proper convex function","level":5,"score":0.5735743641853333},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5539339780807495},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5354348421096802},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5194889307022095},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5080509185791016},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49382004141807556},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4659463167190552},{"id":"https://openalex.org/C6018138","wikidata":"https://www.wikidata.org/wiki/Q332715","display_name":"Absolutely convex set","level":5,"score":0.4597355127334595},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.45797181129455566},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32645782828330994},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24773427844047546},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23545536398887634},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.05721822381019592},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:ami.inf.ucv.ro:article/157","doi":"https://doi.org/10.52846/ami.v31i0.157","is_oa":true,"landing_page_url":"http://inf.ucv.ro/~ami/index.php/ami/article/view/157","pdf_url":"http://inf.ucv.ro/~ami/index.php/ami/article/download/157/154","source":{"id":"https://openalex.org/S2764551600","display_name":"Annals of the University of Craiova Mathematics and Computer Science Series","issn_l":"1223-6934","issn":["1223-6934","2246-9958"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/I97553796","host_organization_name":"University of Craiova","host_organization_lineage":["https://openalex.org/I97553796"],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1223-6934","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:1516639947","doi":null,"is_oa":false,"landing_page_url":"http://inf.ucv.ro/~ami/index.php/ami/article/download/157/154","pdf_url":null,"source":{"id":"https://openalex.org/S2764551600","display_name":"Annals of the University of Craiova Mathematics and Computer Science Series","issn_l":"1223-6934","issn":["1223-6934","2246-9958"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/I97553796","host_organization_name":"University of Craiova","host_organization_lineage":["https://openalex.org/I97553796"],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Annals of the University of Craiova Mathematics and Computer Science Series","raw_type":null}],"best_oa_location":{"id":"pmh:oai:ami.inf.ucv.ro:article/157","doi":"https://doi.org/10.52846/ami.v31i0.157","is_oa":true,"landing_page_url":"http://inf.ucv.ro/~ami/index.php/ami/article/view/157","pdf_url":"http://inf.ucv.ro/~ami/index.php/ami/article/download/157/154","source":{"id":"https://openalex.org/S2764551600","display_name":"Annals of the University of Craiova Mathematics and Computer Science Series","issn_l":"1223-6934","issn":["1223-6934","2246-9958"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":["dongbi-c","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/I97553796","host_organization_name":"University of Craiova","host_organization_lineage":["https://openalex.org/I97553796"],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1223-6934","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1516639947.pdf","grobid_xml":"https://content.openalex.org/works/W1516639947.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W1551360398","https://openalex.org/W1966480644","https://openalex.org/W2088951401"],"related_works":["https://openalex.org/W1527882233","https://openalex.org/W2089735459","https://openalex.org/W2556084237","https://openalex.org/W7152935753","https://openalex.org/W1998727877","https://openalex.org/W2805615243","https://openalex.org/W2065444577","https://openalex.org/W315796958","https://openalex.org/W7099748412","https://openalex.org/W2088951401"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2,6,10,14,23,28,33,37],"necessary":[3],"condition":[4],"for":[5,36],"minimization":[7],"problem":[8],"of":[9,22],"quasiconvex":[11,38],"function":[12],"on":[13],"closed":[15],"convex":[16,25,29],"set.We":[17],"consider":[18],"both":[19],"the":[20],"case":[21],"general":[24],"set":[26,30,35],"and":[27],"defined":[31],"as":[32],"constrained":[34],"lower":[39],"semicontinuous":[40],"function.":[41]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2016-06-24T00:00:00"}