{"id":"https://openalex.org/W2162423280","doi":"https://doi.org/10.1007/s11590-010-0263-1","title":"Classical linear vector optimization duality revisited","display_name":"Classical linear vector optimization duality revisited","publication_year":2010,"publication_date":"2010-11-20","ids":{"openalex":"https://openalex.org/W2162423280","doi":"https://doi.org/10.1007/s11590-010-0263-1","mag":"2162423280"},"language":"en","primary_location":{"id":"doi:10.1007/s11590-010-0263-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-010-0263-1","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1005.1151","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011677215","display_name":"Radu Ioan Bo\u0163","orcid":"https://orcid.org/0000-0002-4469-314X"},"institutions":[{"id":"https://openalex.org/I44260953","display_name":"Heinrich Heine University D\u00fcsseldorf","ror":"https://ror.org/024z2rq82","country_code":"DE","type":"education","lineage":["https://openalex.org/I44260953"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Radu Ioan Bo\u0163","raw_affiliation_strings":["Mathematical Institute, Heinrich-Heine University, Universit\u00e4tsstra\u00dfe 1, 40225, D\u00fcsseldorf, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute, Heinrich-Heine University, Universit\u00e4tsstra\u00dfe 1, 40225, D\u00fcsseldorf, Germany","institution_ids":["https://openalex.org/I44260953"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089451173","display_name":"Sorin\u2010Mihai Grad","orcid":"https://orcid.org/0000-0002-1139-7504"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sorin-Mihai Grad","raw_affiliation_strings":["Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088024629","display_name":"Gert Wanka","orcid":"https://orcid.org/0000-0002-3653-3525"},"institutions":[{"id":"https://openalex.org/I2610724","display_name":"Chemnitz University of Technology","ror":"https://ror.org/00a208s56","country_code":"DE","type":"education","lineage":["https://openalex.org/I2610724"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Gert Wanka","raw_affiliation_strings":["Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Chemnitz University of Technology, 09107, Chemnitz, Germany","institution_ids":["https://openalex.org/I2610724"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011677215"],"corresponding_institution_ids":["https://openalex.org/I44260953"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.6766,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.73302481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"6","issue":"1","first_page":"199","last_page":"210"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9990000128746033,"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/T10567","display_name":"Vehicle Routing Optimization Methods","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing 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":0.8293624520301819},{"id":"https://openalex.org/keywords/vector-optimization","display_name":"Vector optimization","score":0.7942144870758057},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7074964642524719},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.6892106533050537},{"id":"https://openalex.org/keywords/wolfe-duality","display_name":"Wolfe duality","score":0.6265348196029663},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6069000959396362},{"id":"https://openalex.org/keywords/vector-space","display_name":"Vector space","score":0.586001455783844},{"id":"https://openalex.org/keywords/weak-duality","display_name":"Weak duality","score":0.5834295749664307},{"id":"https://openalex.org/keywords/dual-space","display_name":"Dual space","score":0.5665598511695862},{"id":"https://openalex.org/keywords/ordered-vector-space","display_name":"Ordered vector space","score":0.5649952292442322},{"id":"https://openalex.org/keywords/convex-cone","display_name":"Convex cone","score":0.49242934584617615},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.47415369749069214},{"id":"https://openalex.org/keywords/perturbation-function","display_name":"Perturbation function","score":0.46928417682647705},{"id":"https://openalex.org/keywords/normed-vector-space","display_name":"Normed vector space","score":0.45244213938713074},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.42345964908599854},{"id":"https://openalex.org/keywords/dual-pair","display_name":"Dual pair","score":0.41169166564941406},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.3786713480949402},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3643597960472107},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.3380594253540039},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3334847688674927},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.3088889420032501},{"id":"https://openalex.org/keywords/topological-tensor-product","display_name":"Topological tensor product","score":0.11320018768310547}],"concepts":[{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.8293624520301819},{"id":"https://openalex.org/C164088818","wikidata":"https://www.wikidata.org/wiki/Q7917833","display_name":"Vector optimization","level":4,"score":0.7942144870758057},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7074964642524719},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.6892106533050537},{"id":"https://openalex.org/C109456813","wikidata":"https://www.wikidata.org/wiki/Q8029991","display_name":"Wolfe duality","level":5,"score":0.6265348196029663},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6069000959396362},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.586001455783844},{"id":"https://openalex.org/C80682859","wikidata":"https://www.wikidata.org/wiki/Q7977943","display_name":"Weak duality","level":4,"score":0.5834295749664307},{"id":"https://openalex.org/C45633534","wikidata":"https://www.wikidata.org/wiki/Q752487","display_name":"Dual space","level":2,"score":0.5665598511695862},{"id":"https://openalex.org/C113837420","wikidata":"https://www.wikidata.org/wiki/Q1503340","display_name":"Ordered vector space","level":5,"score":0.5649952292442322},{"id":"https://openalex.org/C28340159","wikidata":"https://www.wikidata.org/wiki/Q2256541","display_name":"Convex cone","level":5,"score":0.49242934584617615},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.47415369749069214},{"id":"https://openalex.org/C102144036","wikidata":"https://www.wikidata.org/wiki/Q7170952","display_name":"Perturbation function","level":5,"score":0.46928417682647705},{"id":"https://openalex.org/C171739935","wikidata":"https://www.wikidata.org/wiki/Q726210","display_name":"Normed vector space","level":2,"score":0.45244213938713074},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.42345964908599854},{"id":"https://openalex.org/C198586994","wikidata":"https://www.wikidata.org/wiki/Q96376663","display_name":"Dual pair","level":5,"score":0.41169166564941406},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.3786713480949402},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3643597960472107},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.3380594253540039},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3334847688674927},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.3088889420032501},{"id":"https://openalex.org/C178099376","wikidata":"https://www.wikidata.org/wiki/Q7825044","display_name":"Topological tensor product","level":4,"score":0.11320018768310547},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C6183050","wikidata":"https://www.wikidata.org/wiki/Q3058180","display_name":"Interpolation space","level":4,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C122357587","wikidata":"https://www.wikidata.org/wiki/Q6934508","display_name":"Multi-swarm optimization","level":3,"score":0.0},{"id":"https://openalex.org/C55112680","wikidata":"https://www.wikidata.org/wiki/Q190549","display_name":"Functional analysis","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s11590-010-0263-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11590-010-0263-1","pdf_url":null,"source":{"id":"https://openalex.org/S12647387","display_name":"Optimization Letters","issn_l":"1862-4472","issn":["1862-4472","1862-4480"],"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":"Optimization Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1005.1151","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1005.1151","pdf_url":"https://arxiv.org/pdf/1005.1151","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":{"id":"pmh:oai:arXiv.org:1005.1151","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1005.1151","pdf_url":"https://arxiv.org/pdf/1005.1151","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W5295403","https://openalex.org/W341071838","https://openalex.org/W417516028","https://openalex.org/W631421241","https://openalex.org/W1278184806","https://openalex.org/W1585268704","https://openalex.org/W1971283516","https://openalex.org/W1980976739","https://openalex.org/W1990023680","https://openalex.org/W1991078291","https://openalex.org/W2058732732","https://openalex.org/W2072263460","https://openalex.org/W2139622853","https://openalex.org/W2155011141","https://openalex.org/W2160987576","https://openalex.org/W2253489845","https://openalex.org/W2517749439","https://openalex.org/W4236721833","https://openalex.org/W4249667877"],"related_works":["https://openalex.org/W4313014939","https://openalex.org/W4210245775","https://openalex.org/W2061589448","https://openalex.org/W4220928172","https://openalex.org/W640885572","https://openalex.org/W3213165575","https://openalex.org/W2362763982","https://openalex.org/W2351130384","https://openalex.org/W2136200239","https://openalex.org/W1687657632"],"abstract_inverted_index":null,"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":8}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
