{"id":"https://openalex.org/W2967801541","doi":"https://doi.org/10.3390/axioms8030097","title":"Multiobjective Fractional Symmetric Duality in Mathematical Programming with (C,Gf)-Invexity Assumptions","display_name":"Multiobjective Fractional Symmetric Duality in Mathematical Programming with (C,Gf)-Invexity Assumptions","publication_year":2019,"publication_date":"2019-08-13","ids":{"openalex":"https://openalex.org/W2967801541","doi":"https://doi.org/10.3390/axioms8030097","mag":"2967801541"},"language":"en","primary_location":{"id":"doi:10.3390/axioms8030097","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8030097","pdf_url":"https://www.mdpi.com/2075-1680/8/3/97/pdf?version=1565667657","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/2075-1680/8/3/97/pdf?version=1565667657","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079725730","display_name":"Ramu Dubey","orcid":"https://orcid.org/0000-0001-8434-0907"},"institutions":[{"id":"https://openalex.org/I55124831","display_name":"J.C. Bose University of Science & Technology, YMCA","ror":"https://ror.org/014jqnm52","country_code":"IN","type":"education","lineage":["https://openalex.org/I55124831"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ramu Dubey","raw_affiliation_strings":["Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad 121 006, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad 121 006, India","institution_ids":["https://openalex.org/I55124831"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054777936","display_name":"Lakshmi Narayan Mishra","orcid":"https://orcid.org/0000-0001-7774-7290"},"institutions":[{"id":"https://openalex.org/I876193797","display_name":"Vellore Institute of Technology University","ror":"https://ror.org/00qzypv28","country_code":"IN","type":"education","lineage":["https://openalex.org/I876193797"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Lakshmi Narayan Mishra","raw_affiliation_strings":["Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India"],"raw_orcid":"https://orcid.org/0000-0001-7774-7290","affiliations":[{"raw_affiliation_string":"Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, India","institution_ids":["https://openalex.org/I876193797"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080017749","display_name":"Clemente Cesarano","orcid":"https://orcid.org/0000-0002-1694-7907"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Clemente Cesarano","raw_affiliation_strings":["Section of Mathematics, International Telematic University UNINETTUNO, C.so Vittorio Emanuele II, 3900186 Roma, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section of Mathematics, International Telematic University UNINETTUNO, C.so Vittorio Emanuele II, 3900186 Roma, Italy","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054777936"],"corresponding_institution_ids":["https://openalex.org/I876193797"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":2.0211,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.88080771,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"8","issue":"3","first_page":"97","last_page":"97"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9997000098228455,"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":0.9997000098228455,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9980000257492065,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9803000092506409,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7588446140289307},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6730340719223022},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.638343334197998},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5828196406364441},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5162177085876465},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4794936776161194},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46053624153137207},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.4575045108795166},{"id":"https://openalex.org/keywords/fractional-programming","display_name":"Fractional programming","score":0.4408150315284729},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43758150935173035},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.42404860258102417},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4211893081665039},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19567453861236572},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13444414734840393},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12475377321243286},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.09471109509468079},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.09117835760116577},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.051505059003829956}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7588446140289307},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6730340719223022},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.638343334197998},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5828196406364441},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5162177085876465},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4794936776161194},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46053624153137207},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.4575045108795166},{"id":"https://openalex.org/C169069869","wikidata":"https://www.wikidata.org/wiki/Q5477546","display_name":"Fractional programming","level":4,"score":0.4408150315284729},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43758150935173035},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.42404860258102417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4211893081665039},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19567453861236572},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13444414734840393},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12475377321243286},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.09471109509468079},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.09117835760116577},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.051505059003829956},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms8030097","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8030097","pdf_url":"https://www.mdpi.com/2075-1680/8/3/97/pdf?version=1565667657","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:4fbbc8487fe2456593e00daa180f3be1","is_oa":true,"landing_page_url":"https://doaj.org/article/4fbbc8487fe2456593e00daa180f3be1","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 8, Iss 3, p 97 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/8/3/97/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/axioms8030097","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms8030097","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms8030097","pdf_url":"https://www.mdpi.com/2075-1680/8/3/97/pdf?version=1565667657","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2967801541.pdf","grobid_xml":"https://content.openalex.org/works/W2967801541.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1969573529","https://openalex.org/W1975517593","https://openalex.org/W1979740742","https://openalex.org/W1983666584","https://openalex.org/W1990854574","https://openalex.org/W2000983337","https://openalex.org/W2062360657","https://openalex.org/W2086601312","https://openalex.org/W2170707515","https://openalex.org/W2809970575","https://openalex.org/W2893926553","https://openalex.org/W2941704029","https://openalex.org/W6646265170","https://openalex.org/W6666133679","https://openalex.org/W6753120325","https://openalex.org/W6755273170"],"related_works":["https://openalex.org/W2802888879","https://openalex.org/W2082221223","https://openalex.org/W2018824531","https://openalex.org/W2378272748","https://openalex.org/W2356513498","https://openalex.org/W2353865704","https://openalex.org/W2008967475","https://openalex.org/W2046750649","https://openalex.org/W2348150945","https://openalex.org/W1979316962"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3],"new":[4],"class":[5],"of":[6,26],"(":[7,36,58],"C":[8,59],",":[9,38,60],"G":[10,39,61],"f":[11,40,62],")":[12,41,63],"-invex":[13],"functions":[14],"introduce":[15],"and":[16,53],"give":[17],"nontrivial":[18],"numerical":[19],"examples":[20],"which":[21],"justify":[22],"exist":[23],"such":[24],"type":[25,48],"functions.":[27],"Also,":[28],"we":[29],"construct":[30],"generalized":[31],"convexity":[32],"definitions":[33],"(such":[34],"as,":[35],"F":[37],"-invexity,":[42],"C-convex":[43],"etc.).":[44],"We":[45],"consider":[46],"Mond\u2013Weir":[47],"fractional":[49],"symmetric":[50],"dual":[51],"programs":[52],"derive":[54],"duality":[55],"results":[56,67,71],"under":[57],"-invexity":[64],"assumptions.":[65],"Our":[66],"generalize":[68],"several":[69],"known":[70],"in":[72],"the":[73],"literature.":[74]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2019-08-22T00:00:00"}
