{"id":"https://openalex.org/W2028606028","doi":"https://doi.org/10.1016/s0167-6377(96)00032-6","title":"Duality with multiple criteria and multiple resources","display_name":"Duality with multiple criteria and multiple resources","publication_year":1996,"publication_date":"1996-11-01","ids":{"openalex":"https://openalex.org/W2028606028","doi":"https://doi.org/10.1016/s0167-6377(96)00032-6","mag":"2028606028"},"language":"en","primary_location":{"id":"doi:10.1016/s0167-6377(96)00032-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0167-6377(96)00032-6","pdf_url":null,"source":{"id":"https://openalex.org/S27769002","display_name":"Operations Research Letters","issn_l":"0167-6377","issn":["0167-6377","1872-7468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research Letters","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/A5045105549","display_name":"Aharon Ben\u2010Tal","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Aharon Ben-Tal","raw_affiliation_strings":["Technion \u2014 Faculty of Industrial Engineering and Management, Technion City, Haifa 32000, Israel","Technion Faculty of Industrial Engineering and Management, Technion City, Haifa 32000, Israel#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Technion \u2014 Faculty of Industrial Engineering and Management, Technion City, Haifa 32000, Israel","institution_ids":["https://openalex.org/I174306211"]},{"raw_affiliation_string":"Technion Faculty of Industrial Engineering and Management, Technion City, Haifa 32000, Israel#TAB#","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109486816","display_name":"J\u00f8rgen Tind","orcid":null},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":true,"raw_author_name":"J\u00f8rgen Tind","raw_affiliation_strings":["Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen O, Denmark","Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen \u00d8, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen O, Denmark","institution_ids":["https://openalex.org/I124055696"]},{"raw_affiliation_string":"Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen \u00d8, Denmark","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109486816"],"corresponding_institution_ids":["https://openalex.org/I124055696"],"apc_list":{"value":2760,"currency":"USD","value_usd":2760},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17674204,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"5","first_page":"201","last_page":"206"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9926000237464905,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9926000237464905,"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/T12137","display_name":"Economic theories and models","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9782999753952026,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.8117454051971436},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6342382431030273},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5882924199104309},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5877771973609924},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.5210894346237183},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4824010133743286},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.45539939403533936},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.4401463568210602},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.43849143385887146},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.4354918897151947},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4283347427845001},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.42682385444641113},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.42009931802749634},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.40141189098358154},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.362693190574646},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34889185428619385},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3379512429237366},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3012891709804535},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2292023003101349},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06975355744361877}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.8117454051971436},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6342382431030273},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5882924199104309},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5877771973609924},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.5210894346237183},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4824010133743286},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.45539939403533936},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.4401463568210602},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.43849143385887146},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.4354918897151947},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4283347427845001},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.42682385444641113},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.42009931802749634},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.40141189098358154},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.362693190574646},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34889185428619385},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3379512429237366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3012891709804535},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2292023003101349},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06975355744361877},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0167-6377(96)00032-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0167-6377(96)00032-6","pdf_url":null,"source":{"id":"https://openalex.org/S27769002","display_name":"Operations Research Letters","issn_l":"0167-6377","issn":["0167-6377","1872-7468"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Operations Research Letters","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.49.4322","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.4322","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.ku.dk/~tind/multiresources.ps","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":6,"referenced_works":["https://openalex.org/W625187458","https://openalex.org/W2036737894","https://openalex.org/W2058732732","https://openalex.org/W2153015072","https://openalex.org/W2322316662","https://openalex.org/W4248313157"],"related_works":["https://openalex.org/W4220928172","https://openalex.org/W3213165575","https://openalex.org/W2029896594","https://openalex.org/W4210245775","https://openalex.org/W2056178476","https://openalex.org/W2345066843","https://openalex.org/W4283709143","https://openalex.org/W2136200239","https://openalex.org/W2061589448","https://openalex.org/W2384039353"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
