{"id":"https://openalex.org/W2941704029","doi":"https://doi.org/10.1051/ro/2019044","title":"Symmetric duality results for second-order nondifferentiable multiobjective programming problem","display_name":"Symmetric duality results for second-order nondifferentiable multiobjective programming problem","publication_year":2019,"publication_date":"2019-04-01","ids":{"openalex":"https://openalex.org/W2941704029","doi":"https://doi.org/10.1051/ro/2019044","mag":"2941704029"},"language":"en","primary_location":{"id":"doi:10.1051/ro/2019044","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2019044","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","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/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":true,"raw_author_name":"Ramu Dubey","raw_affiliation_strings":["Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad 121 006, Haryana, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad 121 006, Haryana, India","institution_ids":["https://openalex.org/I55124831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009385455","display_name":"Vishnu Narayan Mishra","orcid":"https://orcid.org/0000-0002-2159-7710"},"institutions":[{"id":"https://openalex.org/I296362101","display_name":"Indira Gandhi National Tribal University","ror":"https://ror.org/04yayy336","country_code":"IN","type":"education","lineage":["https://openalex.org/I296362101"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Vishnu Narayan Mishra","raw_affiliation_strings":["Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484887, India","L. 1627 Awadh Puri Colony Beniganj, Phase III, Opposite Industrial Training Institute (I.T.I.), Ayodhya 224 001, Uttar Pradesh, India"],"raw_orcid":"https://orcid.org/0000-0002-2159-7710","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484887, India","institution_ids":["https://openalex.org/I296362101"]},{"raw_affiliation_string":"L. 1627 Awadh Puri Colony Beniganj, Phase III, Opposite Industrial Training Institute (I.T.I.), Ayodhya 224 001, Uttar Pradesh, India","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079725730"],"corresponding_institution_ids":["https://openalex.org/I55124831"],"apc_list":null,"apc_paid":null,"fwci":2.7995,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.9135684,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"53","issue":"2","first_page":"539","last_page":"558"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9998999834060669,"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":0.9998999834060669,"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9702000021934509,"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":0.8490502834320068},{"id":"https://openalex.org/keywords/multiobjective-programming","display_name":"Multiobjective programming","score":0.6862431764602661},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6764144897460938},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.5628650784492493},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5536714196205139},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.544710099697113},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5010793209075928},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.47896888852119446},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4454551041126251},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4291146397590637},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34406131505966187},{"id":"https://openalex.org/keywords/multi-objective-optimization","display_name":"Multi-objective optimization","score":0.25335320830345154},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.24370485544204712}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.8490502834320068},{"id":"https://openalex.org/C2988952207","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multiobjective programming","level":3,"score":0.6862431764602661},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6764144897460938},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.5628650784492493},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5536714196205139},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.544710099697113},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5010793209075928},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.47896888852119446},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4454551041126251},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4291146397590637},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34406131505966187},{"id":"https://openalex.org/C68781425","wikidata":"https://www.wikidata.org/wiki/Q2052203","display_name":"Multi-objective optimization","level":2,"score":0.25335320830345154},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.24370485544204712},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1051/ro/2019044","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ro/2019044","pdf_url":null,"source":{"id":"https://openalex.org/S20631277","display_name":"RAIRO - Operations Research","issn_l":"0399-0559","issn":["0399-0559","1290-3868"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Operations Research","raw_type":"journal-article"},{"id":"pmh:oai:numdam.org:RO_2019__53_2_539_0","is_oa":false,"landing_page_url":"https://www.numdam.org/articles/10.1051/ro/2019044/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"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":"Text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W190688969","https://openalex.org/W1969919355","https://openalex.org/W1975517593","https://openalex.org/W1976442301","https://openalex.org/W1979740742","https://openalex.org/W1983666584","https://openalex.org/W1983749636","https://openalex.org/W1984854629","https://openalex.org/W1990854574","https://openalex.org/W2011587300","https://openalex.org/W2030467555","https://openalex.org/W2035647929","https://openalex.org/W2043250543","https://openalex.org/W2046715566","https://openalex.org/W2072277727","https://openalex.org/W2095445548","https://openalex.org/W2295543373","https://openalex.org/W2893926553","https://openalex.org/W4251358541"],"related_works":["https://openalex.org/W4210245775","https://openalex.org/W2029896594","https://openalex.org/W3213165575","https://openalex.org/W2056178476","https://openalex.org/W4220928172","https://openalex.org/W2406638882","https://openalex.org/W2040864114","https://openalex.org/W2390707064","https://openalex.org/W1980978552","https://openalex.org/W2045473346"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,30,55],"study":[4],"the":[5,22,52],"existence":[6,23],"of":[7,24,27],"G":[8,11],"f":[9,12],"-bonvex/":[10],"-pseudo-bonvex":[13],"functions":[14],"and":[15,39],"construct":[16],"various":[17],"nontrivial":[18,42],"numerical":[19],"examples":[20],"for":[21],"such":[25],"type":[26,33],"functions.":[28],"Furthermore,":[29],"formulate":[31],"Mond-Weir":[32],"second-order":[34],"nondifferentiable":[35],"multiobjective":[36],"programming":[37],"problem":[38],"give":[40],"a":[41],"concrete":[43],"example":[44],"which":[45],"justify":[46],"weak":[47],"duality":[48,58],"theorem":[49],"present":[50],"in":[51],"paper.":[53],"Next,":[54],"prove":[56],"appropriate":[57],"relations":[59],"under":[60],"aforesaid":[61],"assumptions.":[62]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
