{"id":"https://openalex.org/W2059380444","doi":"https://doi.org/10.1137/060676398","title":"Duality in Linear Programming Problems Related to Deterministic Long Run Average Problems of Optimal Control","display_name":"Duality in Linear Programming Problems Related to Deterministic Long Run Average Problems of Optimal Control","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2059380444","doi":"https://doi.org/10.1137/060676398","mag":"2059380444"},"language":"en","primary_location":{"id":"doi:10.1137/060676398","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060676398","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","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/A5059691564","display_name":"Luke Finlay","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Luke Finlay","raw_affiliation_strings":["luke.finlay@unisa.edu.au and v.gaitsgory@unisa.edu.au#TAB#"],"affiliations":[{"raw_affiliation_string":"luke.finlay@unisa.edu.au and v.gaitsgory@unisa.edu.au#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017737718","display_name":"Vladimir Gaitsgory","orcid":"https://orcid.org/0000-0002-9174-4560"},"institutions":[{"id":"https://openalex.org/I170239107","display_name":"University of South Australia","ror":"https://ror.org/01p93h210","country_code":"AU","type":"education","lineage":["https://openalex.org/I170239107"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Vladimir Gaitsgory","raw_affiliation_strings":["University of South Australia"],"affiliations":[{"raw_affiliation_string":"University of South Australia","institution_ids":["https://openalex.org/I170239107"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040071859","display_name":"Ivan Lebedev","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ivan Lebedev","raw_affiliation_strings":["ilebedev@workcover.com#TAB#"],"affiliations":[{"raw_affiliation_string":"ilebedev@workcover.com#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059691564"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0675,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.87019638,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"47","issue":"4","first_page":"1667","last_page":"1700"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9979000091552734,"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":0.9979000091552734,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9821000099182129,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9707000255584717,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.7854725122451782},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.7735663652420044},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7338763475418091},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6025547981262207},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5371841192245483},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5087264180183411},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4894186556339264},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.48708462715148926},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.1515301764011383},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12976643443107605}],"concepts":[{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.7854725122451782},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.7735663652420044},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7338763475418091},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6025547981262207},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5371841192245483},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5087264180183411},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4894186556339264},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.48708462715148926},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.1515301764011383},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12976643443107605},{"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":2,"locations":[{"id":"doi:10.1137/060676398","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060676398","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:urm_publish:9915911150101831","is_oa":false,"landing_page_url":"https://hdl.handle.net/1959.8/71841","pdf_url":null,"source":{"id":"https://openalex.org/S4306402528","display_name":"UniSA Research Outputs Repository (University of South Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I170239107","host_organization_name":"University of South Australia","host_organization_lineage":["https://openalex.org/I170239107"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":56,"referenced_works":["https://openalex.org/W261814290","https://openalex.org/W307801612","https://openalex.org/W357773498","https://openalex.org/W565681979","https://openalex.org/W642634611","https://openalex.org/W1481789702","https://openalex.org/W1487586009","https://openalex.org/W1490150974","https://openalex.org/W1507296508","https://openalex.org/W1529558080","https://openalex.org/W1551529843","https://openalex.org/W1558902221","https://openalex.org/W1583562272","https://openalex.org/W1596039783","https://openalex.org/W1963793715","https://openalex.org/W1964377184","https://openalex.org/W1964771320","https://openalex.org/W1967281297","https://openalex.org/W1968203684","https://openalex.org/W1973312554","https://openalex.org/W1975083310","https://openalex.org/W1976237319","https://openalex.org/W1976578591","https://openalex.org/W1985096926","https://openalex.org/W1990337648","https://openalex.org/W1994103282","https://openalex.org/W2006003117","https://openalex.org/W2009060269","https://openalex.org/W2012507994","https://openalex.org/W2018895295","https://openalex.org/W2031875106","https://openalex.org/W2033049721","https://openalex.org/W2041336415","https://openalex.org/W2054625457","https://openalex.org/W2056945084","https://openalex.org/W2058080504","https://openalex.org/W2062736751","https://openalex.org/W2068098627","https://openalex.org/W2079867004","https://openalex.org/W2085068326","https://openalex.org/W2086412293","https://openalex.org/W2088348409","https://openalex.org/W2088807940","https://openalex.org/W2091472813","https://openalex.org/W2096491608","https://openalex.org/W2101019468","https://openalex.org/W2104004905","https://openalex.org/W2111893470","https://openalex.org/W2122073174","https://openalex.org/W2127470768","https://openalex.org/W2128515424","https://openalex.org/W2133707954","https://openalex.org/W2484199605","https://openalex.org/W2596682183","https://openalex.org/W2928176981","https://openalex.org/W3038830718"],"related_works":["https://openalex.org/W2760715419","https://openalex.org/W2020677672","https://openalex.org/W2793446615","https://openalex.org/W2523699569","https://openalex.org/W4324270384","https://openalex.org/W2171781592","https://openalex.org/W2030099148","https://openalex.org/W2020065878","https://openalex.org/W1984009044","https://openalex.org/W2032341808"],"abstract_inverted_index":{"It":[0],"has":[1],"been":[2],"established":[3],"recently":[4],"that,":[5],"under":[6],"mild":[7],"conditions,":[8],"deterministic":[9],"long":[10],"run":[11],"average":[12],"problems":[13,24,47],"of":[14,57,60,69],"optimal":[15,71],"control":[16],"are":[17],"\u201casymptotically":[18],"equivalent\u201d":[19],"to":[20],"infinite-dimensional":[21],"linear":[22],"programming":[23],"(LPPs)":[25],"and":[26,44,48,63],"that":[27],"these":[28],"LPPs":[29,62],"can":[30],"be":[31],"approximated":[32],"by":[33],"finite-dimensional":[34,45,61],"LPPs.":[35],"In":[36],"this":[37],"paper":[38],"we":[39],"introduce":[40],"the":[41,55,70],"corresponding":[42],"infinite-":[43],"dual":[46],"study":[49],"duality":[50],"relationships.":[51],"We":[52],"also":[53],"investigate":[54],"possibility":[56],"using":[58],"solutions":[59],"their":[64],"duals":[65],"for":[66],"numerical":[67,83],"construction":[68,78],"controls":[72],"in":[73],"periodic":[74],"optimization":[75],"problems.":[76],"The":[77],"is":[79],"illustrated":[80],"with":[81],"a":[82],"example.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}