{"id":"https://openalex.org/W2053602861","doi":"https://doi.org/10.1155/2013/708979","title":"Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems","display_name":"Optimality Conditions and Duality of Three Kinds of Nonlinear Fractional Programming Problems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2053602861","doi":"https://doi.org/10.1155/2013/708979","mag":"2053602861"},"language":"lv","primary_location":{"id":"doi:10.1155/2013/708979","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/708979","pdf_url":"https://downloads.hindawi.com/journals/aor/2013/708979.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/aor/2013/708979.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100332103","display_name":"Xiaomin Zhang","orcid":"https://orcid.org/0000-0001-6345-4235"},"institutions":[{"id":"https://openalex.org/I24201400","display_name":"Chengdu University of Information Technology","ror":"https://ror.org/01yxwrh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I24201400"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiaomin Zhang","raw_affiliation_strings":["Department of Mathematics, Chengdu University of Information Technology, Sichuan 610225, China"],"raw_orcid":"https://orcid.org/0000-0001-6345-4235","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chengdu University of Information Technology, Sichuan 610225, China","institution_ids":["https://openalex.org/I24201400"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101795007","display_name":"Zezhong Wu","orcid":"https://orcid.org/0000-0003-2444-6421"},"institutions":[{"id":"https://openalex.org/I24201400","display_name":"Chengdu University of Information Technology","ror":"https://ror.org/01yxwrh59","country_code":"CN","type":"education","lineage":["https://openalex.org/I24201400"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zezhong Wu","raw_affiliation_strings":["Department of Mathematics, Chengdu University of Information Technology, Sichuan 610225, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Chengdu University of Information Technology, Sichuan 610225, China","institution_ids":["https://openalex.org/I24201400"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100332103"],"corresponding_institution_ids":["https://openalex.org/I24201400"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.3724,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.65375234,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"9"},"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9927999973297119,"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"}},{"id":"https://openalex.org/T12709","display_name":"Optimization and Mathematical Programming","score":0.9799000024795532,"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/algorithm","display_name":"Algorithm","score":0.6413493156433105},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3665122389793396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32284533977508545}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6413493156433105},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3665122389793396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32284533977508545}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/708979","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/708979","pdf_url":"https://downloads.hindawi.com/journals/aor/2013/708979.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnlaor:708979","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/AOR/2013/708979.xml","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"},{"id":"pmh:oai:doaj.org/article:65e3a8fcae284bafb5e3f5ad89755c37","is_oa":true,"landing_page_url":"https://doaj.org/article/65e3a8fcae284bafb5e3f5ad89755c37","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advances in Operations Research, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/708979","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/708979","pdf_url":"https://downloads.hindawi.com/journals/aor/2013/708979.pdf","source":{"id":"https://openalex.org/S33782831","display_name":"Advances in Operations Research","issn_l":"1687-9147","issn":["1687-9147","1687-9155"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Operations Research","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311826","display_name":"Chengdu University of Information Technology","ror":"https://ror.org/01yxwrh59"},{"id":"https://openalex.org/F4320328111","display_name":"Chengdu University","ror":"https://ror.org/034z67559"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2053602861.pdf","grobid_xml":"https://content.openalex.org/works/W2053602861.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1502437643","https://openalex.org/W1607950902","https://openalex.org/W1966378893","https://openalex.org/W2024600755","https://openalex.org/W2088942587","https://openalex.org/W2091704788","https://openalex.org/W2108077586","https://openalex.org/W2142506503","https://openalex.org/W2313488898"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109"],"abstract_inverted_index":{"Some":[0],"assumptions":[1],"for":[2],"the":[3,12],"objective":[4],"functions":[5,8],"and":[6,16,39,54],"constraint":[7],"are":[9,20,43],"given":[10],"under":[11],"conditions":[13,38],"of":[14,35],"convex":[15],"generalized":[17],"convex,":[18],"which":[19],"based":[21],"on":[22],"the<mml:math":[23],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[24,26,29,46,50,56],"id=\"M1\"><mml:mrow><mml:mi>F</mml:mi></mml:mrow></mml:math>-convex,<mml:math":[25],"id=\"M2\"><mml:mrow><mml:mi>\u03c1</mml:mi></mml:mrow></mml:math>-convex,":[27],"and<mml:math":[28],"id=\"M3\"><mml:mo":[30],"stretchy=\"false\">(</mml:mo><mml:mi>F</mml:mi><mml:mo>,</mml:mo><mml:mi>\u03c1</mml:mi><mml:mo":[31,48],"stretchy=\"false\">)</mml:mo></mml:math>-convex.":[32],"The":[33],"sufficiency":[34],"Kuhn-Tucker":[36],"optimality":[37],"appropriate":[40],"duality":[41],"results":[42],"proved":[44],"involving<mml:math":[45],"id=\"M4\"><mml:mo":[47],"stretchy=\"false\">)</mml:mo></mml:math>-convex,<mml:math":[49],"id=\"M5\"><mml:mo":[51],"stretchy=\"false\">(</mml:mo><mml:mi>F</mml:mi><mml:mo>,</mml:mo><mml:mi>\u03b1</mml:mi><mml:mo>,</mml:mo><mml:mi>\u03c1</mml:mi><mml:mo>,</mml:mo><mml:mi>d</mml:mi><mml:mo":[52,58],"stretchy=\"false\">)</mml:mo></mml:math>-convex,":[53],"generalized<mml:math":[55],"id=\"M6\"><mml:mo":[57],"stretchy=\"false\">)</mml:mo></mml:math>-convex":[59],"functions.":[60]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}
