{"id":"https://openalex.org/W4383722636","doi":"https://doi.org/10.3390/axioms12070673","title":"Robust Optimality Conditions for a Class of Fractional Optimization Problems","display_name":"Robust Optimality Conditions for a Class of Fractional Optimization Problems","publication_year":2023,"publication_date":"2023-07-07","ids":{"openalex":"https://openalex.org/W4383722636","doi":"https://doi.org/10.3390/axioms12070673"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12070673","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070673","pdf_url":"https://www.mdpi.com/2075-1680/12/7/673/pdf?version=1688807562","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/7/673/pdf?version=1688807562","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012641009","display_name":"Tareq Saeed","orcid":"https://orcid.org/0000-0002-0170-5286"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Tareq Saeed","raw_affiliation_strings":["Financial Mathematics and Actuarial Science (FMAS)\u2014Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-0170-5286","affiliations":[{"raw_affiliation_string":"Financial Mathematics and Actuarial Science (FMAS)\u2014Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5012641009"],"corresponding_institution_ids":["https://openalex.org/I185163786"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.5576,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70235717,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"12","issue":"7","first_page":"673","last_page":"673"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9980000257492065,"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":0.9980000257492065,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/convexity","display_name":"Convexity","score":0.7938032150268555},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.7476411461830139},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6864745020866394},{"id":"https://openalex.org/keywords/robust-optimization","display_name":"Robust optimization","score":0.6572493314743042},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6466957330703735},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.571062445640564},{"id":"https://openalex.org/keywords/karush\u2013kuhn\u2013tucker-conditions","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","score":0.5399631857872009},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.513034462928772},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.375122606754303},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3667007088661194},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.08030912280082703},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07221493124961853},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06790423393249512}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7938032150268555},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.7476411461830139},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6864745020866394},{"id":"https://openalex.org/C193254401","wikidata":"https://www.wikidata.org/wiki/Q2160088","display_name":"Robust optimization","level":2,"score":0.6572493314743042},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6466957330703735},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.571062445640564},{"id":"https://openalex.org/C50454189","wikidata":"https://www.wikidata.org/wiki/Q2075125","display_name":"Karush\u2013Kuhn\u2013Tucker conditions","level":2,"score":0.5399631857872009},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.513034462928772},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.375122606754303},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3667007088661194},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.08030912280082703},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07221493124961853},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06790423393249512},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12070673","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070673","pdf_url":"https://www.mdpi.com/2075-1680/12/7/673/pdf?version=1688807562","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:61498c66f96e418d80c110479ed92bf8","is_oa":true,"landing_page_url":"https://doaj.org/article/61498c66f96e418d80c110479ed92bf8","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":"Axioms, Vol 12, Iss 7, p 673 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/7/673/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12070673","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 12; Issue 7; Pages: 673","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12070673","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070673","pdf_url":"https://www.mdpi.com/2075-1680/12/7/673/pdf?version=1688807562","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4383722636.pdf"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1925097415","https://openalex.org/W1967956032","https://openalex.org/W1975786310","https://openalex.org/W2066956585","https://openalex.org/W2076694117","https://openalex.org/W2077853600","https://openalex.org/W2103632601","https://openalex.org/W2400485862","https://openalex.org/W2405251713","https://openalex.org/W2556990173","https://openalex.org/W2744494937","https://openalex.org/W2806781878","https://openalex.org/W2949952486","https://openalex.org/W3044692847","https://openalex.org/W3088573467","https://openalex.org/W3165513546","https://openalex.org/W3175046435","https://openalex.org/W3198116908","https://openalex.org/W3211344532","https://openalex.org/W3216735700","https://openalex.org/W4220928172","https://openalex.org/W4224881304","https://openalex.org/W6644312626"],"related_works":["https://openalex.org/W1993702234","https://openalex.org/W2807256486","https://openalex.org/W2391309548","https://openalex.org/W2123675486","https://openalex.org/W117224218","https://openalex.org/W3038961962","https://openalex.org/W2947894078","https://openalex.org/W2791039104","https://openalex.org/W3164429027","https://openalex.org/W2950961269"],"abstract_inverted_index":{"In":[0,48],"this":[1],"paper,":[2],"by":[3,37],"considering":[4,38],"the":[5,20,27,39,45,52],"parametric":[6],"technique,":[7],"we":[8],"study":[9],"a":[10],"class":[11],"of":[12,44],"fractional":[13],"optimization":[14],"problems":[15],"involving":[16],"data":[17],"uncertainty":[18],"in":[19],"objective":[21],"functional.":[22],"We":[23],"formulate":[24],"and":[25,33],"prove":[26],"robust":[28],"Karush-Kuhn-Tucker":[29],"necessary":[30],"optimality":[31],"conditions":[32],"provide":[34],"their":[35],"sufficiency":[36],"convexity":[40],"and/or":[41],"concavity":[42],"assumptions":[43],"involved":[46],"functionals.":[47],"addition,":[49],"to":[50],"complete":[51],"study,":[53],"an":[54],"illustrative":[55],"example":[56],"is":[57],"presented.":[58]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-10-10T00:00:00"}