{"id":"https://openalex.org/W1966390395","doi":"https://doi.org/10.1142/s0219198904000046","title":"AN EXTENSION OF LEITMANN'S DIRECT METHOD TO INEQUALITY CONSTRAINTS","display_name":"AN EXTENSION OF LEITMANN'S DIRECT METHOD TO INEQUALITY CONSTRAINTS","publication_year":2004,"publication_date":"2004-03-01","ids":{"openalex":"https://openalex.org/W1966390395","doi":"https://doi.org/10.1142/s0219198904000046","mag":"1966390395"},"language":"en","primary_location":{"id":"doi:10.1142/s0219198904000046","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219198904000046","pdf_url":null,"source":{"id":"https://openalex.org/S130757258","display_name":"International Game Theory Review","issn_l":"0219-1989","issn":["0219-1989","1793-6675"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Game Theory Review","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/A5012791135","display_name":"Pierre Cartigny","orcid":null},"institutions":[{"id":"https://openalex.org/I4210129108","display_name":"Groupement de Recherche en \u00c9conomie Quantitative d\u2019Aix-Marseille","ror":"https://ror.org/02ek9wp67","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210129108","https://openalex.org/I4210142724","https://openalex.org/I4210150854","https://openalex.org/I90669466"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"PIERRE CARTIGNY","raw_affiliation_strings":["INRA Montpellier and GREQAM, Centre de la Vieille Charit\u00e9, 2 rue de la Charit\u00e9, 13002 Marseille, France"],"affiliations":[{"raw_affiliation_string":"INRA Montpellier and GREQAM, Centre de la Vieille Charit\u00e9, 2 rue de la Charit\u00e9, 13002 Marseille, France","institution_ids":["https://openalex.org/I4210129108"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044818025","display_name":"Christophe Deissenberg","orcid":"https://orcid.org/0000-0001-7473-5649"},"institutions":[{"id":"https://openalex.org/I4210129108","display_name":"Groupement de Recherche en \u00c9conomie Quantitative d\u2019Aix-Marseille","ror":"https://ror.org/02ek9wp67","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I21491767","https://openalex.org/I4210129108","https://openalex.org/I4210142724","https://openalex.org/I4210150854","https://openalex.org/I90669466"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"CHRISTOPHE DEISSENBERG","raw_affiliation_strings":["GREQAM and Department of Economics, Universit\u00e9de la M\u00e9diterran\u00e9e, Ch\u00e2teau La Farge, Route des Milles, 13290 Les Milles, France"],"affiliations":[{"raw_affiliation_string":"GREQAM and Department of Economics, Universit\u00e9de la M\u00e9diterran\u00e9e, Ch\u00e2teau La Farge, Route des Milles, 13290 Les Milles, France","institution_ids":["https://openalex.org/I4210129108"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012791135"],"corresponding_institution_ids":["https://openalex.org/I4210129108"],"apc_list":null,"apc_paid":null,"fwci":0.3457,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59073276,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"06","issue":"01","first_page":"15","last_page":"20"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9933000206947327,"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":0.9933000206947327,"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":0.9746000170707703,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9740999937057495,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/extension","display_name":"Extension (predicate logic)","score":0.8035078048706055},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6377810835838318},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.6206979751586914},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.5970713496208191},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.5376739501953125},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5256941318511963},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5119841694831848},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39272546768188477},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2494845986366272},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14867621660232544}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.8035078048706055},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6377810835838318},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6206979751586914},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.5970713496208191},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.5376739501953125},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5256941318511963},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5119841694831848},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39272546768188477},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2494845986366272},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14867621660232544},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0219198904000046","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219198904000046","pdf_url":null,"source":{"id":"https://openalex.org/S130757258","display_name":"International Game Theory Review","issn_l":"0219-1989","issn":["0219-1989","1793-6675"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Game Theory Review","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:igtrxx:v:06:y:2004:i:01:n:s0219198904000046","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S0219198904000046","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:RePEc:wsi:igtrxx:v:06:y:2004:i:01:p:15-20","is_oa":false,"landing_page_url":"http://www.worldscinet.com/cgi-bin/details.cgi?type=html&id=pii:S0219198904000046","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6700000166893005,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W12435090","https://openalex.org/W1972995776","https://openalex.org/W2067301884","https://openalex.org/W4249062545"],"related_works":["https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W2369178846","https://openalex.org/W2082716031","https://openalex.org/W2370289839","https://openalex.org/W2933494595","https://openalex.org/W1568049691","https://openalex.org/W1590096425","https://openalex.org/W2909053289","https://openalex.org/W2901122627"],"abstract_inverted_index":{"George":[0],"Leitmann's":[1],"direct":[2],"method":[3,27],"permits":[4],"to":[5,28],"find":[6],"the":[7],"global":[8],"minimum":[9],"of":[10,16,19,31],"a":[11,17,29],"variational":[12],"problem":[13],"by":[14],"use":[15],"change":[18],"variables.":[20],"In":[21],"this":[22,26],"article,":[23],"we":[24],"extend":[25],"class":[30],"scalar,":[32],"inequality":[33],"constrained":[34],"problems.":[35],"An":[36],"application":[37],"example":[38],"is":[39],"given.":[40]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}