{"id":"https://openalex.org/W2051158553","doi":"https://doi.org/10.1007/bf01259337","title":"A note about linear inequality systems and duality","display_name":"A note about linear inequality systems and duality","publication_year":1987,"publication_date":"1987-05-01","ids":{"openalex":"https://openalex.org/W2051158553","doi":"https://doi.org/10.1007/bf01259337","mag":"2051158553"},"language":"en","primary_location":{"id":"doi:10.1007/bf01259337","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01259337","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":"Zeitschrift f\ufffdr 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/A5016160092","display_name":"Miguel \u00c1. Goberna","orcid":"https://orcid.org/0000-0002-5363-7991"},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"M. A. Goberna","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Alicante, 03071, Alicante, Spain","Department of Mathematics and Statistics, University of Alicante, Alicante, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Alicante, 03071, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Alicante, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043570540","display_name":"V. Jornet","orcid":null},"institutions":[{"id":"https://openalex.org/I130194489","display_name":"University of Alicante","ror":"https://ror.org/05t8bcz72","country_code":"ES","type":"education","lineage":["https://openalex.org/I130194489"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"V. Jornet","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Alicante, 03071, Alicante, Spain","Department of Mathematics and Statistics, University of Alicante, Alicante, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Alicante, 03071, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Alicante, Alicante, Spain","institution_ids":["https://openalex.org/I130194489"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130194489"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.2063172,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"31","issue":"3","first_page":"A71","last_page":"A78"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.998199999332428,"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":0.998199999332428,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9973999857902527,"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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/converse","display_name":"Converse","score":0.8369569778442383},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7546305656433105},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.721108615398407},{"id":"https://openalex.org/keywords/linear-inequality","display_name":"Linear inequality","score":0.6956052780151367},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4746589958667755},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4459892213344574},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.44562190771102905},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.44062840938568115},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.437055379152298},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4360755383968353},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4159350097179413},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.41414526104927063},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.41234180331230164},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.39294564723968506},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39160382747650146},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34726405143737793},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2467018961906433},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21642345190048218},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.20696651935577393},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13474178314208984},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.052164942026138306}],"concepts":[{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.8369569778442383},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7546305656433105},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.721108615398407},{"id":"https://openalex.org/C84135550","wikidata":"https://www.wikidata.org/wiki/Q3154022","display_name":"Linear inequality","level":3,"score":0.6956052780151367},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4746589958667755},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4459892213344574},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.44562190771102905},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.44062840938568115},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.437055379152298},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4360755383968353},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4159350097179413},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.41414526104927063},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.41234180331230164},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.39294564723968506},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39160382747650146},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34726405143737793},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2467018961906433},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21642345190048218},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.20696651935577393},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13474178314208984},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.052164942026138306},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf01259337","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf01259337","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":"Zeitschrift f\ufffdr Operations Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.550000011920929,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W14127467","https://openalex.org/W70102910","https://openalex.org/W76236552","https://openalex.org/W1523693682","https://openalex.org/W1980355224","https://openalex.org/W1983601864","https://openalex.org/W1989721897","https://openalex.org/W2047133484","https://openalex.org/W2069235686"],"related_works":["https://openalex.org/W2376997122","https://openalex.org/W2026600343","https://openalex.org/W2391247224","https://openalex.org/W2112761337","https://openalex.org/W4382519084","https://openalex.org/W4311073519","https://openalex.org/W144566582","https://openalex.org/W2002037426","https://openalex.org/W4288640859","https://openalex.org/W3092518081"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
