{"id":"https://openalex.org/W1975578510","doi":"https://doi.org/10.1007/s12351-015-0172-2","title":"Sufficiency and duality for optimization problems involving interval-valued invex functions in parametric form","display_name":"Sufficiency and duality for optimization problems involving interval-valued invex functions in parametric form","publication_year":2015,"publication_date":"2015-03-12","ids":{"openalex":"https://openalex.org/W1975578510","doi":"https://doi.org/10.1007/s12351-015-0172-2","mag":"1975578510"},"language":"en","primary_location":{"id":"doi:10.1007/s12351-015-0172-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12351-015-0172-2","pdf_url":null,"source":{"id":"https://openalex.org/S140563256","display_name":"Operational Research","issn_l":"1109-2858","issn":["1109-2858","1866-1505"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operational 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/A5087624087","display_name":"Anurag Jayswal","orcid":"https://orcid.org/0000-0001-6715-087X"},"institutions":[{"id":"https://openalex.org/I189109744","display_name":"Indian Institute of Technology Dhanbad","ror":"https://ror.org/013v3cc28","country_code":"IN","type":"education","lineage":["https://openalex.org/I189109744"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Anurag Jayswal","raw_affiliation_strings":["Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826 004, Jharkhand, India","Department of Applied Mathematics, Indian School of Mines, Dhanbad, India;"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826 004, Jharkhand, India","institution_ids":["https://openalex.org/I189109744"]},{"raw_affiliation_string":"Department of Applied Mathematics, Indian School of Mines, Dhanbad, India;","institution_ids":["https://openalex.org/I189109744"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108232657","display_name":"Ioan Stancu-Minasian","orcid":null},"institutions":[{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Ioan Stancu-Minasian","raw_affiliation_strings":["Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 13 Septembrie Street, No. 13, 050711, Bucharest, Romania","Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Bucharest, Romania#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 13 Septembrie Street, No. 13, 050711, Bucharest, Romania","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Bucharest, Romania#TAB#","institution_ids":["https://openalex.org/I58077936"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089500544","display_name":"Jonaki Banerjee","orcid":null},"institutions":[{"id":"https://openalex.org/I189109744","display_name":"Indian Institute of Technology Dhanbad","ror":"https://ror.org/013v3cc28","country_code":"IN","type":"education","lineage":["https://openalex.org/I189109744"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Jonaki Banerjee","raw_affiliation_strings":["Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826 004, Jharkhand, India","Department of Applied Mathematics, Indian School of Mines, Dhanbad, India;"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Indian School of Mines, Dhanbad, 826 004, Jharkhand, India","institution_ids":["https://openalex.org/I189109744"]},{"raw_affiliation_string":"Department of Applied Mathematics, Indian School of Mines, Dhanbad, India;","institution_ids":["https://openalex.org/I189109744"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000192932","display_name":"Andreea M\u0103d\u0103lina Stancu","orcid":null},"institutions":[{"id":"https://openalex.org/I58077936","display_name":"Romanian Academy","ror":"https://ror.org/0561n6946","country_code":"RO","type":"archive","lineage":["https://openalex.org/I58077936"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Andreea Madalina Stancu","raw_affiliation_strings":["Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 13 Septembrie Street, No. 13, 050711, Bucharest, Romania","Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Bucharest, Romania#TAB#"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 13 Septembrie Street, No. 13, 050711, Bucharest, Romania","institution_ids":["https://openalex.org/I58077936"]},{"raw_affiliation_string":"Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, Bucharest, Romania#TAB#","institution_ids":["https://openalex.org/I58077936"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5087624087"],"corresponding_institution_ids":["https://openalex.org/I189109744"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.1827,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.87877733,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"1","first_page":"137","last_page":"161"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9984999895095825,"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":0.9984999895095825,"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":0.9965999722480774,"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/T10969","display_name":"Water resources management and optimization","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/dual-polyhedron","display_name":"Dual polyhedron","score":0.8425172567367554},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.8225751519203186},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6740586757659912},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.6370431184768677},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.5828486084938049},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.5431898832321167},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.4927220642566681},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.4841111898422241},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47027379274368286},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4241487681865692},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.402060329914093},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.3705461025238037},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3061474859714508},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.197702556848526},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17173096537590027}],"concepts":[{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.8425172567367554},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.8225751519203186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6740586757659912},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.6370431184768677},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.5828486084938049},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5431898832321167},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.4927220642566681},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.4841111898422241},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47027379274368286},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4241487681865692},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.402060329914093},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3705461025238037},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3061474859714508},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.197702556848526},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17173096537590027},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12351-015-0172-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12351-015-0172-2","pdf_url":null,"source":{"id":"https://openalex.org/S140563256","display_name":"Operational Research","issn_l":"1109-2858","issn":["1109-2858","1866-1505"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operational Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W76919318","https://openalex.org/W113792361","https://openalex.org/W201137195","https://openalex.org/W1522916005","https://openalex.org/W1580809199","https://openalex.org/W1967779834","https://openalex.org/W1981882279","https://openalex.org/W1995290830","https://openalex.org/W2003644018","https://openalex.org/W2009054772","https://openalex.org/W2011900172","https://openalex.org/W2013374813","https://openalex.org/W2032705969","https://openalex.org/W2041782481","https://openalex.org/W2051792233","https://openalex.org/W2055103090","https://openalex.org/W2059708052","https://openalex.org/W2073833672","https://openalex.org/W2081484590","https://openalex.org/W2083592805","https://openalex.org/W2119289347","https://openalex.org/W2231208742","https://openalex.org/W4233868504","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W4220928172","https://openalex.org/W2725387418","https://openalex.org/W2201555914","https://openalex.org/W3213165575","https://openalex.org/W1821047009","https://openalex.org/W2038258422","https://openalex.org/W2136200239","https://openalex.org/W2080941243","https://openalex.org/W1687657632","https://openalex.org/W2091041828"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
