{"id":"https://openalex.org/W2159283875","doi":"https://doi.org/10.1007/bf01417520","title":"On duality in the vectorial control-approximation problem","display_name":"On duality in the vectorial control-approximation problem","publication_year":1991,"publication_date":"1991-07-01","ids":{"openalex":"https://openalex.org/W2159283875","doi":"https://doi.org/10.1007/bf01417520","mag":"2159283875"},"language":"en","primary_location":{"id":"doi:10.1007/bf01417520","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01417520","pdf_url":null,"source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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":"ZOR Zeitschrift f\ufffd Operations Research Methods and Models of 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/A5088024629","display_name":"Gert Wanka","orcid":"https://orcid.org/0000-0002-3653-3525"},"institutions":[{"id":"https://openalex.org/I2802534935","display_name":"Merseburg University of Applied Sciences","ror":"https://ror.org/04f8x5b20","country_code":"DE","type":"education","lineage":["https://openalex.org/I2802534935"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"G. Wanka","raw_affiliation_strings":["Sektion Mathematik, Technische Hochschule \u201cCarl Schorlemmer\u201d Leuna-Merseburg, Otto-Nuschke-Stra\u00dfe, O-4200, Merseburg, FRG","Sektion Mathematik, Technische Hochschule \u201cCarl Schorlemmer\u201d Leuna-Merseburg, Merseburg, FRG"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sektion Mathematik, Technische Hochschule \u201cCarl Schorlemmer\u201d Leuna-Merseburg, Otto-Nuschke-Stra\u00dfe, O-4200, Merseburg, FRG","institution_ids":["https://openalex.org/I2802534935"]},{"raw_affiliation_string":"Sektion Mathematik, Technische Hochschule \u201cCarl Schorlemmer\u201d Leuna-Merseburg, Merseburg, FRG","institution_ids":["https://openalex.org/I2802534935"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088024629"],"corresponding_institution_ids":["https://openalex.org/I2802534935"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.5563,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.90753948,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"35","issue":"4","first_page":"309","last_page":"320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9987999796867371,"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":0.9987999796867371,"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/T11545","display_name":"Advanced Banach Space Theory","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11777","display_name":"Fixed Point Theorems Analysis","score":0.9721999764442444,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.809135913848877},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.5812155604362488},{"id":"https://openalex.org/keywords/reflexivity","display_name":"Reflexivity","score":0.5780041813850403},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5540996193885803},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5401946306228638},{"id":"https://openalex.org/keywords/strong-duality","display_name":"Strong duality","score":0.5189996957778931},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.5063825845718384},{"id":"https://openalex.org/keywords/duality-gap","display_name":"Duality gap","score":0.5018110275268555},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.500199556350708},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41448983550071716},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33381935954093933},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3229856491088867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30737489461898804},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.27322202920913696},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.0696655809879303},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06807547807693481}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.809135913848877},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5812155604362488},{"id":"https://openalex.org/C13200473","wikidata":"https://www.wikidata.org/wiki/Q2747831","display_name":"Reflexivity","level":2,"score":0.5780041813850403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5540996193885803},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5401946306228638},{"id":"https://openalex.org/C163863214","wikidata":"https://www.wikidata.org/wiki/Q7624553","display_name":"Strong duality","level":3,"score":0.5189996957778931},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.5063825845718384},{"id":"https://openalex.org/C5274546","wikidata":"https://www.wikidata.org/wiki/Q5310264","display_name":"Duality gap","level":3,"score":0.5018110275268555},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.500199556350708},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41448983550071716},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33381935954093933},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3229856491088867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30737489461898804},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.27322202920913696},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0696655809879303},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06807547807693481},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"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/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01417520","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01417520","pdf_url":null,"source":{"id":"https://openalex.org/S126160977","display_name":"Mathematical Methods of Operations Research","issn_l":"1432-2994","issn":["1432-2994","1432-5217"],"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":"ZOR Zeitschrift f\ufffd Operations Research Methods and Models of Operations Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1503047656","https://openalex.org/W1506922153","https://openalex.org/W1653619892","https://openalex.org/W1993247264","https://openalex.org/W2019618539","https://openalex.org/W2036062327","https://openalex.org/W2048901266","https://openalex.org/W2056722395","https://openalex.org/W2056723044","https://openalex.org/W2064441376","https://openalex.org/W2069104637","https://openalex.org/W2083818478","https://openalex.org/W2086601312","https://openalex.org/W2118103640","https://openalex.org/W2153015072","https://openalex.org/W2208323839","https://openalex.org/W4252052822","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/W2614523486","https://openalex.org/W2136200239","https://openalex.org/W1821047009","https://openalex.org/W2038258422","https://openalex.org/W2080941243","https://openalex.org/W1687657632"],"abstract_inverted_index":null,"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}